# Seminars (HRT)

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Event When Speaker Title Presentation Material
HRT 3rd September 2008
15:00 to 16:00
Near-wall streaks

This abstract is being written after the talk. The talk was planned as a report on recent results. Instead, it became a rather informal discussion of the approach to predicting streaks advocated in (Chernyshenko & Baig, The mechanism of streak formation in near-wall turbulence, J. Fluid Mech. 2005, V.544, pp.99-131). It is appropriate, therefore, simply to state the main ideas put forward and discussed.

The approach is based on linearised equations but applies to fully-developed turbulent flow, which is non-linear. The reason why linearised equations apply to nonlinear turbulence can be explained in the following way. The full (non-linear) Navier-Stokes equations can be rewritten in terms of perturbations, u’, with all the terms occurring in the linearised equations placed in the left-hand side and all other terms in the right-hand side: Lu’=N[u’]. The non-linear operator N acts as a mixer, conserving energy but destroying structure. The linear operator L acts as a filter-amplifier, amplifying particular structures (streaks) and filtering out the rest (so that the total energy remains constant). Hence, streaks can be predicted by studying L. One way of studying its properties is to solve an optimization problem: maximize ||u’|| for fixed ||Lu’||. From the mathematical viewpoint this leads to a version of the optimal perturbation problem and is related to non-normality and transient growth. However, the interpretation given above requires that the norm of u’ should measure the property of the solution which is being predicted. For predicting streak spacing at a certain distance from the wall this should be the energy of u’ measured within a plane at that distance from the wall. Such an approach proved to have significant predictive ability. Note also that the optimal perturbation solution itself is not a model of the developed turbulent flow but rather a means to investigate the properties of L. More details can be found in the paper cited.

HRT 4th September 2008
15:00 to 16:00
Turbulent mixing as a self-convolution process
HRTW01 8th September 2008
10:00 to 11:00
Wall-Bounded Turbulence: Introduction
HRTW01 8th September 2008
11:30 to 12:30
Introduction - Transition
HRTW01 8th September 2008
14:00 to 14:20
S Chernyshenko Ten questions to facilitate discussions during the workshop

Turbulence research is distinguished by its complexity making rigorous results scarce. This comparative lack of objectivity is a matter of concern for the turbulence research community, even though it does consist of most brilliant and creative researchers. Logic standards are best maintained in face-to-face discussions, for which the present workshop provides an excellent opportunity. The desire to use it in full motivates this talk. Several questions linking seemingly unrelated results are suggested for discussion below.

HRTW01 8th September 2008
14:20 to 14:40
N Nikitin Universal character of perturbation growth in near-wall turbulence
Spatial instability of fully developed turbulent flow in a long straight circular pipe is investigated via DNS. The incompressible Navier-Stokes equations are solved with turbulent inflow velocity field extracted from auxiliary streamwise-periodic simulation which run in parallel with the main spatial simulation. In addition, small perturbations are introduced into the inlet and velocity difference between the flows with and without perturbations is analyzed. It is shown that mean perturbation amplitude $\varepsilon$ increases exponentially with distance downstream until saturating at the level comparable to the level of turbulent fluctuations in the flow. The rate of the exponential growth is found to be constant when normalized by viscous length, $\varepsilon\sim\exp(0.002x^+)$ over the considered Reynolds number range $140\leqslant\Re_\tau \leqslant320$. The universal character of perturbation growth is confirmed also by channel flow simulations.
HRTW01 8th September 2008
14:40 to 15:00
S Chen Reynolds-stress-constrained subgrid-scale stress model for large eddy simulation of wall bounded turbulent flow
In the traditional hybrid RANS/LES approaches for the simulation of wall-bounded fluid turbulence, such as the detached eddy simulation (DES), the whole flow domain is divided into the inner layer and outer layer. Typically the Reynolds averaged Navier-Stokes (RANS) equation is used for the inner layer, while the large eddy simulation (LES) is used for the outer layer. The transition from the inner layer solution to the outer layer is often problematic due to lacking small scale dynamics in the RANS region. In this paper we propose to simulate the whole flow region by large eddy simulation while enforcing a RANS Reynolds stress for the inner layer. We verifed our approach by simulating three-dimensional turbulent channel flows. We were able to accurately model the mean velocity and the turbulent stress using the same grid size as DES. The application of the proposed constrained LES to other turbulent flows with separation will also be discussed.
HRTW01 8th September 2008
15:30 to 15:50
JC Vassilicos The Karman constant is inversely proportional to the number of stagnation points at the upper edge of the buffer layer and is therefore not a universal constant

By an adaptation of the Rice theorem to three-dimensional incompressible vector fields we show that the average distance between turbulent velocity stagnation points at a certain distance from the wall is proportional to the Taylor microscale at that distance. Then, by using this result in conjunction with the balance between kinetic energy dissipation and production in the log-layer we calculate the Karman constant as a function of other constants. We show that the Karman constant is inversely proportional to the number of turbulent velocity stagnation points at the edge of the log-layer that is closest to the wall.

We perform three different Direct Numerical Simulations (DNS) of fully developed turbulent channel flows to test our formula. In two of these DNS the flow is forced at the wall in two different ways and in the remaining third simulation it is not. The proportionality between the inverse Karman constant and the number $C_s$ of turbulent velocity stagnation points at the upper edge of the buffer layer is observed in all three simulations even though the values of the Karman constant and $C_s$ are different in each one of these simulations. Our formula is therefore able to predict and explain why the Karman constant is not a universal constant.

HRTW01 8th September 2008
15:50 to 16:10
Non-universality of the Von Kármán "constant"
The overlap parameters of the logarithmic region in turbulent pipe, channel, and boundary-layer flows are established using a composite profile approach which incorporates the influence of the outer part. The $Re$-specific von Kármán coefficient for channel flows decreases with Reynolds number to a level below the well defined value of $\kappa_{BZ}~=~0.384$ for ZPG TBLs. The proper limiting value of $\kappa_C$ for the channel flow could not be established with a high confidence because of the limited range of available Reynolds numbers, but the best projected value is near $\kappa_C\sim 0.37$. For the pipe flow, reprocessing of the Superpipe data indicates that $\kappa_P\sim0.41$, which on the opposite side of the boundary layer value compared to the channel flow. This collective behavior of $\kappa$ in boundary layers, pipes and channels suggests that the von Kármán coefficient is not universal, and exhibits dependence on not only the pressure gradient but also on the flow geometry, thereby raising fundamental questions regarding turbulence flow theory and modeling for all wall-bounded flows. In contrast, a wide range of data from such canonical flows reveals a universal relation between the overlap parameters; i.e., the von Kármán coefficient and the intercept B.
HRTW01 8th September 2008
16:10 to 16:30
Comparison between turbulent boundary layers and channels from direct numerical simulations
Preliminary results are presented from a new simulation of the zero-pressure-gradient turbulent boundary layer at Re_\theta=1000-2100, which are compared to simulations of turbulent channels at similar Reynolds numbers. Even the low order statistic differ considerably between the two flows, including for some quantities the values within the buffer layer. In general the pressure and the transverse velocity fluctuations are stronger in boundary layers than in channels, even if the wall-parallel scales that can be derived from the spectra and the two-point correlations are simular in both cases. On the other hand, the streamwise fluctuation intensities are roughly similar in both flows, but their scales are shorter and narrower in boundary layers than in channels. The difference between the two flows is traced to an excess of production of the streamwise turbulent energy in the outer part of the boundary layers compared to channels (by a factor of order two), which is associated with the presence of a stronger wake component of the mean velocity profile. Most of this excess production is compensated by stronger pressure fluctuations and by the pressure-strain term, whicht redistribute the energy to the transverse components. The difference in the statistic can be traced in experimental results at higher Reynolds numbers, although qunatities such as the pressure fluctuations and the energy budgets are not available for them. These results suggest that caution should be used in mixing different flows when document, for example, Reynolds number effects in shear turbulence.
HRTW01 8th September 2008
16:50 to 17:10
A simple model for the log-law region of a boundary layer
We build on the work of Davidson, Krogstad & Nickels (JFM, 2006) and propose an elementary model for the log-law region of a boundary-layer. The model is remarkably simple, contains only one free parameter, and assumes very little about the shape of the boundary-layer eddies. The physical content of the model is simple: we assume that the two-point statistics of the streamwise velocity fluctuations know about the presence of the wall only to the extent that, over a range of eddy sizes, it imposes a kinetic energy scale proportional to the square of the shear velocity. Little else is assumed. Despite its naivety, the model is an excellent fit to experimental data for the k-1 law of the one-dimensional, longitudinal spectrum, F11(k), and also to F11(k), in the inertial range. It is also an excellent fit to experimental data for the real-space analogue of the k-1 law; that is, the logarithmic law for the longitudinal structure-function.
HRTW01 8th September 2008
17:10 to 17:30
Modelling large-scale influences in near-wall turbulence
Turbulent boundary layers are traditionally considered in terms of an inner and outer region, not excluding the logarithmic region, which is usually identified with an overlap of the two regions. Recent experiments in high Reynolds number flows have revealed that the key to understanding the scaling behaviour of the turbulence statistics lies in unravelling the influence and interaction of the outer and inner regions. In this talk a model for the influence of the large-scale motions in wall turbulence (termed “superstructures”) on the inner viscous region is presented. The model has implications for predicting wall-shear stress fluctuations based on a filtered velocity signature in the outer part of the boundary layer, as required in high Reynolds number large-eddy simulations.
HRTW01 9th September 2008
09:40 to 10:00
Transition to turbulence in pipe flow
According to textbook wisdom, flow down a pipe becomes turbulent near a Reynolds number of about 2000. This simple statement misses many subtleties of the transition: the absence of a linear stability of the laminar flow, the sensitive dependence on perturbations that sometimes succeed and sometimes fail to induce turbulence and the unexpected observation that the turbulent state, once achieved, is not persistent but can decay. All these observations are compatible with the formation of a strange saddle in the state space of the system. I will focus on three aspects: on the appearance of 3-d coherent states, on the information contained in lifetime statistics and on results on the boundary between laminar and turbulent regions. They suggest a generic structuring of state space in flows where turbulent and laminar flow coexist.
HRTW01 9th September 2008
10:00 to 10:20
B Hof Repeller or attractor? Selecting the dynamical model of shear flow turbulence
The collapse of turbulence, observable in shear flows at low Reynolds numbers, raises the question if turbulence is generically of transient nature or becomes sustained at some critical point. Recent data have lead to conflicting views with the majority of studies supporting the model of turbulence turning into an attracting state. Here we present lifetime measurements of turbulence in pipe flow spanning eight orders of magnitude in time, drastically extending all previous investigations. We show that no critical point exists in this regime and that in contrast to the prevailing view the turbulent state remains transient. The observed transient scaling behaviour has been conjectured to occur in turbulent flows more than two decades ago.
HRTW01 9th September 2008
10:20 to 10:40
Optimal paths to transition in a duct
It is accepted that self sustaining states exist in duct flow past a threshold value of the Reynolds number, which rely on the nonlinear coupling between vortices, streaks and travelling waves. In this work we have devised an optimisation strategy that aims at maximising the energy of the travelling disturbance wave, and thus at enhancing the nonlinear terms that feed back onto vortices and streaks.
HRTW01 9th September 2008
10:40 to 11:00
Investigating puffs in square duct flow
We are investigating the characteristics of localized disturbances in the flow through a straight duct with a square cross-section. For this purpose, we have performed pseudo-spectral DNS in streamwise periodic domains with a length of 100 duct half-widths. By imposing a body force locally and for a finite temporal interval (similar to the work in a pipe by Willis & Kerswell, Phys. Rev. Lett. 98/100, 2007/2008), a 'puff' is generated when the bulk Reynolds number (based upon the half width) is chosen within the range of approximately 800 to 1000; for lower values the disturbance decays, whereas for higher values the puff expands and ends up filling the entire periodic domain. We have followed the evolution of equilibrium puffs for several thousand bulk time units, enabling us to compute the statistics of the perturbed flow. Phase-locked averaging has been performed in order to reveal the internal structure of the puffs.
HRTW01 9th September 2008
11:30 to 11:50
Invariant solutions and visualization of dynamics in plane Couette flow
It has recently become possible to compute precise equilibrium, traveling wave, and periodic orbit solutions to pipe and plane Couette flow at moderate Reynolds numbers. These invariant solutions capture the complex dynamics of rolls and streaks (coherent structures) in wall-bounded flows and provide a framework for understanding turbulent flows as dynamical systems. We present (1) a number of weakly unstable equilibria, traveling waves, and periodic orbits of plane Couette flow, (2) visualizations of their physical and state-space dynamics, and (3) statistics on how frequently the solutions appear within turbulent flows. What emerges is a picture of moderate-Reynolds turbulence as a walk among a set of weakly unstable invariant solutions.
HRTW01 9th September 2008
11:50 to 12:10
Symmetry reduced averages over moderately turbulent flows
Long-term averages in low-dimensional dynamical systems can be expressed as averages over invariant state-space sets (equilibria, periodic orbits, partially hyperbolic invariant tori). We speculate as to how such theory might work for moderately turbulent flows.
HRTW01 9th September 2008
12:10 to 12:30
P Manneville Transitional plane Couette flow: an alternative to the low dimensional dynamical systems approach
The transition from the turbulent state to the laminar regime in plane Couette flow is studied by means of a model focusing on the in-plane (x,z) space dependence of a few velocity amplitudes with reduced wall-normal (y) dependence. The model appears well suited to study the low-R transitional range. I shall present my latest results obtained at very large aspect ratio (typically 768x768 with gap rescaled to 1) and attempt to convince people that the statistical physics of spatiotemporal chaos in extended geometry offers a valuable alternative to the well-accepted interpretation of the relaxation of turbulence in terms of chaotic transients typical of low-dimensional dynamical systems.
HRTW01 9th September 2008
14:00 to 14:20
A mechanism for turbulent drag reduction by polymers

Minute quantities of long chained polymers, of order 10 ppm, added to liquids like water or oil are capable of cutting the turbulent wall friction by half. This startling effect- the "Toms phenomenon" -has been known for more than 60 years, but a detailed explanation of how such small amounts of polymer alter the structure of turbulence so dramatically has been lacking. To explore this question, direct numerical simulations have been performed based on a visco-elastic model of the fluid that uses a finite extensible non-linear elastic-Peterlin (FENE-P) constituitive equation. It is found that the stresses due to the polymers circulating around turbulent vortices produce counter-torques that inherently oppose the rotation. Vortices creating the turbulent transport responsible for drag are weakened and the creation of new vortices is inhibited. Thus, both coherent and incoherent turbulent Reynolds stresses are reduced. Interesting, the viscoelastic stresses of the FENE-P model rely upon the vortices being asymmetric and such deviations from axisymmetry occur where the vortices are strained by themselves or by adjacent vortices.

Kim, K, Li, C.-F., Sureshkumar, R., Balachandar, S. and Adrian, R. J., “Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow,” J. Fluid Mech. 584, 281 (2007).

Kim, K,, Adrian, R. J., Balachandar, S. and Sureshkumar, R., “Dynamics of hairpin vortices and polymer-induced turbulent drag reduction,” Phys Rev. Lett. 100 (2008). LJ11563

HRTW01 9th September 2008
14:20 to 14:40
J Kim Physics and control of wall turbulence
It has been generally accepted that nonlinearity is an essential characteristic of turbulent flows. Consequently, except for special situations in which a linear mechanism is expected to play a dominant role (e.g., rapidly straining turbulent flows to which the rapid distortion theory can be applied), the role of linear mechanisms in turbulent flows has not received much attention. Even for transitional flows, a common notion is that the most a linear theory can provide is insight into the early stages of transition to turbulence. But several investigators have recently shown that linear mechanisms play an important role even in fully turbulent, and hence fully nonlinear, flows. Examples of such studies include: optimal disturbances in turbulent boundary layers (Butler \& Farrell 1993); transient growth due to non-normality of the Navier-Stokes system (Reddy \& Henningson 1993); applications of a linear control theory to transitional and turbulent channel flows (Joshi \etal 1997); and a numerical experiment (Kim \& Lim 2000) demonstrating that near-wall turbulence could not be maintained in turbulent channel flow when a linear mechanism was artificially suppressed. \medskip Turbulent channel flow is analyzed from a linear system point of view. After recasting the linearized Navier-Stokes equations into a state-space representation, the singular value decomposition (SVD) analysis is applied to the linear system, with and without control input, in order to gain new insight into the mechanism by which various controllers are able to accomplish the viscous drag reduction in turbulent boundary layers. We examine linear-quadratic-regulator (LQR) controllers that we have used, as well as the opposition control of Choi \etal (1994), which has been a benchmark for comparison of various control strategies. The performance of control is examined in terms of the largest singular values, which represent the maximum disturbance energy growth ratio attainable in the linear system under control. The SVD analysis shows a similarity between the trend observed in the SVD analysis (linear) and that observed in direct numerical simulations (nonlinear), thus reaffirming the importance of linear mechanisms in the near-wall dynamics of turbulent boundary layers. It is shown that the SVD analysis of the linearized system can indeed provide useful insight into the performance of linear controllers. Other issues, such as the effect of using the evolving mean flow as control applied to a nonlinear flow system (a.k.a. gain scheduling) and high Reynolds-number limitation, can be also investigated through the SVD analysis. Finally, time permitting, a linear Floquet analysis of a channel flow with periodic control, which had been shown to sustain skin-friction drag below that of a laminar channel, will be discussed to elucidate the drag reducing mechanism.
HRTW01 9th September 2008
14:40 to 15:00
Input-output analysis, model reduction and flow control applied to the Blasius boundary layer
The dynamics and control of disturbances in the spatially evolving boundary layer on a flat-plate are investigated from an input-output viewpoint. From the linearized Navier-Stokes equations with inputs (disturbances and actuators) and outputs (objective function and sensor) controllable, observable and balanced modes are extracted using the snapshot-method and a matrix-free time-stepper approach. A balanced reduced-order model is constructed and shown to capture the input-output behaviour of linearized Navier-Stokes equations. This model is used to design a LQG-feedback controller to suppress the growth of perturbations inside the boundary layer
HRTW01 9th September 2008
15:30 to 15:50
Optimal transient growth and very large scale structures in turbulent boundary layers
The optimal energy growth of perturbations sustained by a zero pressure gradient turbulent boundary is computed using the eddy viscosity associated with the turbulent mean flow. It is found that even if all the considered turbulent mean profiles are linearly stable, they support transient energy growths. The most amplified perturbations are streamwise uniform and correspond to streamwise streaks originated by streamwise vortices. For sufficiently large Reynolds numbers two distinct peaks of the optimal growth exist respectively scaling in inner and outer units. The optimal structures associated with the peak scaling in inner units correspond well to the most probable streaks and vortices observed in the buffer layer and their moderate energy growth is independent of the Reynolds number. The energy growth associated with the peak scaling in outer units is larger than that of the inner peak and scales linearly with an effective turbulent Reynolds number formed with the maximum eddy viscosity and a modified Rotta-Clauser length based on the momentum thickness. The corresponding optimal perturbations consist in very large scale structures with a spanwise wavelength of the order of 8 $\delta$. The associated optimal streaks scale in outer variables in the outer region and in wall units in the inner region of the boundary layer, there being proportional to the mean flow velocity. These outer streaks protrude far into the near wall region, having still 50% of their maximum amplitude at $y^+=20$. The amplification of very large scale structures appears to be a robust feature of the turbulent boundary layer: Optimal perturbations with spanwise wavelengths ranging from 4 to 15 $\delta$ can all reach 80% of the overall optimal peak growth.
HRTW01 9th September 2008
15:50 to 16:10
Genesis of coherent structures through an interactive bypass transition process
The interaction between two localized disturbances is analyzed in a subcritical channel flow through direct numerical simulations. The initial perturbations are in the form of two pairs of counter rotating vortices. One of them interacts with the wall normal vorticity layers set-up near the wall, by compressing or stretching locally part of them through the straining motion it induces. The breakdown of spanwise symmetry leads to the rapid development of a new wall normal vorticity patch that is tilted by the shear and rolls up into a new small-scale streamwise vortex. The process results in a localized turbulent spot at later stages of development. A detailed analysis is carried out to determine the role of different parameters entering in the physics of the mechanism. Several critical thresholds that trigger the interactive bypass transition process are found and analyzed. The similitude parameters resulting from the parametric investigation coincide well with those governing the self-sustaining Reynolds shear stress producing eddies in the buffer layer of a fully developed turbulent wall flow. It is suggested that the mechanism we propose may play some role in the regeneration cycle of the near wall turbulence generating structures by precisely bypassing the three-dimensional streak instability mechanism. An active strategy based on this process is applied to the mixing in microsystems. The specific interactions asymmetrically distributed in space lead to a better mixing locally in time and space leading to the possibility of active control of scalar transport in micro devices.
HRTW01 9th September 2008
16:10 to 16:30
The Reynolds shear stress in zero pressure gradient turbulent boundary layers
The Reynolds shear stress (RS) in zero pressure gradient turbulent boundary layers is established using recently developed composite mean velocity profiles based on the “log-law” in the overlap region between inner and outer profiles. The contribution of the normal stress difference is also considered and shown to be relatively small. From this analysis, an asymptotic expansion for the maximum RS and its location is developed. The hypotheses underlying this analysis are discussed and the results are compared with experiments and DNS. Using the friction velocity as scale, the RS determined from composite mean velocity profiles agrees reasonably well with low-Re experimental results. However, when comparing with high-Re experiments and DNS, the agreement is generally limited as near the wall the experimental accuracy and resolution becomes problematic and far from the wall the numerical treatment of the boundary condition is very delicate.
HRTW01 9th September 2008
16:30 to 16:50
GL Eyink Turbulent flow in pipes and channels as cross-stream inverse cascades of vorticity
A commonplace view of pressure-driven turbulence in pipes and channels is as “cascades” of streamwise momentum toward the viscous layer at the wall. We present in this talk an alternative picture of these flows as “inverse cascades” of spanwise vorticity, in the cross-stream direction but away from the viscous sublayer. We show that there is a constant spatial flux of spanwise vorticity, due to vorticity conservation, and that this flux is necessary to produce pressure-drop and energy dissipation. The vorticity transport is shown to be dominated by viscous diffusion at distances closer to the wall than the peak Reynolds stress, well into the classical log-layer. The Perry-Chong model based on “representative" hairpin /horseshoe vortices predicts a single sign of the turbulent vorticity flux over the whole log-layer, whereas the actual flux must change sign at the location of the Reynolds-stress maximum. The Perry-Chong model may be viable at distances beyond the peak. The vortex-cascade picture presented here has a close analogue in the theory of quantum superfluids and superconductors, the “phase slippage” of quantized vortex lines. Most of our results should therefore apply as well to superfluid turbulence in pipes and channels. We also discuss issues about drag-reduction from this perspective.
HRTW01 10th September 2008
09:40 to 10:00
Implications of Ekman layer DNS for near wall similarity
HRTW01 10th September 2008
10:00 to 10:20
On very long structures in boundary layers
The existence, structure and statistics of very long structures in boundary layers will be discussed with particular reference to their three dimensional structure and the extent to which they can be explained as chance concatentations of shorter structures.
HRTW01 10th September 2008
10:20 to 10:40
Lagrangian measurements of inertial particle accelerations in shear, and in grid generated turbulence
We describe two dimensional Lagrangian acceleration statistics of inertial particles in a turbulent boundary layer and contrast the results with those observed in decaying grid generated turbulence (Ayyalasomayajula PRL .Vol. 97,144507 (2006)) . The statistics were determined by means of particle tracking techniques using a high speed camera moving along the side of a wind tunnel at the mean flow speed . Water droplets were fed into the flow using two different methods: sprays placed down-stream from an active grid, and from tubes fed into the boundary layer from humidifiers. The boundary layer, which had considerable free stream turbulence, was formed above a flat plate placed horizontally in the tunnel. The flows are described in terms of the Stokes, Froude and Reynolds numbers. For the flow conditions studied, the sprays produced Stokes numbers varying from 0.47 to 1.2, and the humidifiers produced Stokes numbers varying from 0.035 to 0.25, where the low and high values refer to the outer boundary layer edge and the near-wall region, respectively. The Froude number was approximately 1.0 for the sprays and 0.25 for the humidifiers. The boundary layer momentum thickness Reynolds number was approximately 800. The free stream turbulence was varied by operating the grid in the active mode as well as a passive mode (the latter behaves as a conventional grid). The effects of the free stream turbulence on the acceleration statistics were systematically studied. At the outer edge of the boundary layer, where the shear was weak, the acceleration probability density functions were similar to those previously observed in isotropic turbulence for inertial particles. As the boundary layer plate was approached, the tails of the probability density functions narrowed, became negatively skewed, and their peak occurred at negative accelerations (decelerations in the stream-wise direction). The mean deceleration and its rms increased to large values close to the plate. These effects were more pronounced at higher Stokes number. Although there were free stream turbulence effects, and the complex boundary layer structure played an important role, a simple model suggests that the acceleration behavior is dominated by shear and inertia. The results are contrasted with inertial particles in isotropic turbulence and with fluid particle acceleration statistics in a boundary layer. The work was supported by the US National Science Foundation.
HRTW01 10th September 2008
10:40 to 11:00
Significance of localized vortical disturbances in wall-bounded and free shear flows
The resemblance among coherent structures naturally occurring in fully developed bounded turbulent shear flows, transitional flows and free shear layers suggests the existence of a basic mechanism responsible for the formation of the structures under various base flow conditions. The common elements in all such flows are the shear of the base flow and the presence of a localized vortical disturbance within this shear. Due to their localization in space, the surrounding base flow can be assumed to have homogeneous shear to leading order. In this talk we combine analytical, numerical and experimental tools to show that indeed the interaction between a localized dipole-vortical disturbance and the surrounding simple' laminar shear flow where the velocity vector is (at most) a linear function of the coordinates, can reproduce the generation mechanism and characteristics of the coherent structures that naturally occur in turbulent bounded shear flows (counter-rotating vortex pairs and hairpin vortices) and free shear layers (rib vortices').
HRTW01 10th September 2008
11:30 to 11:50
R Durbin Boundary layer transition by discrete and continuous modes
The natural and bypass routes to boundary layer turbulence have traditionally been studied independently. One can characterize our study as an exploration of the situation in which both occur. Experiments indicate that this may be pertinent in certain flow regimes, particularly in adverse pressure gradients. We study this case by direct numerical simulation (DNS). The inflow condition is a superposition of a 3-D continuous mode and a 2-D T-S wave onto a Blasius mean flow. The T-S and continuous modes are obtained by solving the Orr-Sommerfeld and Squire equations by well established numerical methods. The DNS is accomplished with a finite volume, staggered mesh, fractional step algorithm for incompressible Navier-Stokes equations. Either mode, of itself, is unable to provoke transition. With both modes present, transition usually occurred within the computational domain. Transition was preceded by the appearance of Lambda-shaped velocity contours. Although this is reminiscent of secondary instability of T-S waves, the lateral spacing between Lambda's was very much narrower and seemed to be controlled by spanwise wavelength in the continuous mode. However, the spacing and wavelength were not necessarily equal. Two broad classes of behavior were seen, as epitomized by modes 2 and 5. In mode 2 the Lambda's were grouped in staggered rows. The elements of a row are pairs Lambda's. The pairs are aligned in $z$ within the row, which is followed by another row of pairs, shifted horizontally half way between the previous row. Flow visualization will be presented. The lateral spacing between Lambda's within a row is equal to that of the continuous mode --- actually of the perturbation jets spawned by the continuous mode. Mode 5 produced a more irregular pattern, but still arranged in pairs Lambda's. Unlike mode 2, their spanwise spacing differs from that of the continuous mode; it appears to be about three times as wide. Another curious aspect of mode 5 is that a larger streak amplitude can delay transition. Mode 2 shows transition to move upstream as the Klebanoff streaks get stronger. Mode 5 initially promotes transition, then, as its amplitude increases further, it delays transition.
HRTW01 10th September 2008
11:50 to 12:10
Transient growth induced by surface roughness in a Blasius boundary layer
Introduction There has been much recent interest in transient growth both theoretically [1-4] and experimentally [2,5]. The present work stems from an interest in model reduction for flow control: starting with a linear physical model representative of near-wall turbulence, the aim of this experiment is to devise a wall-based estimator. The inviscid transient growth instability has an optimal form of spanwise periodic streamwise vortices resulting in high/low – speed streaks. Slow growth and decay in x and spanwise periodicity suggest a reduced requirement for mode observability. Equations (1) and (2) describe the generation of optimal modes through the coupling term, , viz. Experimental Arrangement The Blasius base flow is developed on a vertical cast aluminium plate with a sharp leading edge in a very low-turbulence intensity (around 0.05%) wind tunnel. A periodic array of roughness elements at 200 mm from the leading edge is used to perturb the base state and introduces steady steamwise vortex pairs approximating the optimum mode. The height, k, spanwise separation, Δz and diameter, d, of the roughness elements are all adjustable. For the present work, 0.5 ≤ k ≤ 1.5, 10 ≤ Δz ≤ 30 and 2.5 ≤ d ≤ 5.0 mm and the measurements are conducted over the central six elements. Two hot wires, one normal and one slanted by 45 degrees to the mean flow, are used to obtain u and w in the range 250 ≤ x ≤ 700 mm. Results and Discussion Figure 1 present typical results for these experiments. Figure 1(a) shows the u-disturbance spectra as a function of spanwise-wavenumber. The spectrum is taken at the wall-normal location where the maximum rms of the disturbance occurs below that predicted by theory [3]. For this case, the first harmonic of the disturbance introduced is discernible for the first four streamwise locations. The energy of the disturbance is observed to grow at the first streamwise location and peaks when \beta is equal to 0.45 before it decays monotonically. Figures 1(b) and (c) show the corresponding disturbance contours at x = 300. The double positive peaks in the u-disturbance merge into a single peak further downstream of the roughness elements. The shape of the w-disturbance is more complicated and suggests that the streamwise vortices produced by the roughness elements are very weak by this location. The u-component of the disturbance shows the effects of a spanwise shear at larger x, the shear increasing with streak amplitudes. In common with other experiments [2,5], the evolution of the disturbance shows significant deviation to that predicted by theory, suggesting a suboptimal initial growth. This raises questions regarding the receptivity mechanism of laminar boundary layers subjected to different types of perturbations, such as free stream turbulence or wall roughness [6]. In future work, we intend to investigate this further as well as estimating the v component from continuity. Simultaneous measurements of the two components of surface skin friction will also be made to enable the design of an estimator for control by surface deformation.
HRTW01 10th September 2008
12:10 to 12:30
R Govindarajan Instabilities in variable-property flows, and the continuous spectrum
The stability work to be presented here is motivated by our ongoing numerical study of vortex merger in the presence of density-stratification. We find that very strong density stratification (even stable'' stratification) can (a) prevent the merger and (b) cause the vortices to break up. At low diffusivity levels the latter results from an inviscid instability due to alternately-signed density jumps packed in a known pattern. The analytical solution yields several co-existing unstable modes, and transient growth can add significantly to the linear growth at moderate times, thus speeding up the break-up of a single vortex. A related problem of Couette-Poiseuille flow and its continuous spectrum in the presence of low levels of base-flow vorticity will be discussed.
HRTW01 10th September 2008
14:00 to 14:20
L Tuckerman Turbulent-laminar patterns in plane Couette flow
Plane Couette flow near transition displays steady periodic oblique bands of alternating turbulent and laminar flow. Numerical simulations of the Navier-Stokes equations in a tilted domain show a rich variety of such patterns, including spatio-temporal intermittency, branching and travelling states, and localized states analogous to spots. Quantitative analysis of the Reynolds-averaged equations reveals that both the mean flow and the turbulent force are centrosymmetric and can be described by only three trigonometric functions, leading to a model of 6 ODEs. The transition is best described as a bifurcation in the probability distribution function of the first Fourier component.
HRTW01 10th September 2008
14:20 to 14:40
Turbulent-laminar patterns II
In this talk extensions of the earlier work on turbulent-laminar patterns will be presented. In particular large-scale computations of turbulent-laminar coexistence in pipe flow will be presented for pipes up to 400 diameters in length.
HRTW01 10th September 2008
14:40 to 15:00
Turbulent dynamics of pipe flows captured in a reduced model
Significant success has been achieved in recent years by a dynamical systems approach to low Reynolds number turbulence, particularly regarding transition and their relation to coherent structures. Establishing links with experiments and simulations of turbulent flows, however, has been stifled by the vastness of the number of degrees of freedom in real flows. This both serves to mask the underlying dynamics and renders the simulations expensive. In plane Couette flows the Minimal Flow Unit was introduced as a testing ground for probing transitional dynamics. For pipe flow we introduce a 2.5-dimensional model which preserves the key spatio-temporal features -- localised puffs, expanding slugs, and long-term transients. Simulations within this model are already proving fruitful in directing parallel simulations in 3-dimensions, which would otherwise prove costly to run without a clear target.
HRTW01 10th September 2008
15:30 to 15:50
Structure and dynamics of turbulent pipe flow
Results of a proper orthogonal decomposition of a turbulent pipe flow generated by direct numerical simulation are presented. The flow field is decomposed into its optimal basis functions as found by solving a Fredholm integral whose kernel is the two-point velocity autocorrelation tensor. The energy, structure, and dynamics of the basis functions are examined. The basis functions are categorised into two classes and six subclasses based on their wavenumber and coherent vorticity structure, and compared to similar results found in turbulent channel flow. The turbulent pipe flow is generated by a direct numerical simulation of the Navier-Stokes equations using a spectral element algorithm at a Reynolds number Re_tau=150 and a domain length of ten diameters (L/D=10). Evidence of very-large-scale motions will also be presented, as well as preliminary results from a corresponding investigation using a new large-domain (L/D=100) simulation.
HRTW01 10th September 2008
15:50 to 16:10
Dynamical characterization of large scale structures in channel flow turbulence
We obtained unstable periodic solutions up to at Re=6000 and travelling wave solution up to at Re=12,000 of streamwise-minimal channel flow by he shooting method. These solutions are on the basin boundary of the turbulent attractor and have characteristics of large scale motions observed in ully-developed channel flow turbulence. We show that these unstable solutions well describe the temporal evolution of the large scale motion embeded in turbulence that is defined by the local minima of streamwise velocity averaged over the streamwise direction.
HRTW01 10th September 2008
16:10 to 16:30
Lower-branch travelling waves and transition to turbulence in pipe flow
Transition to turbulence in cylindrical pipe flow is still not a well understood phenomenon. However, Direct numerical simulation in pipes with periodic boundary conditions shares a lot of common features with recent experiments. Here we are interested in the structure of the laminar-turbulent boundary, the manifold in phase-space separating the initial conditions leading to turbulence from those who lead to quick relaminarisation. Depending on the symmetries of the problem, phase-space trajectories on this manifold approach transiently various travelling wave solutions sitting on it. We can study the implications of this on the transition problem for both short and long pipes.
HRTW01 10th September 2008
16:50 to 17:10
Underlying large-scale structures in transitional pipe flow
Pipe flow undergoes transition to turbulence despite the linear stability of its basic laminar solution. Finite amplitude solutions in the form of travelling waves (H. Faisst and B. Eckhardt, Phys. Rev. Lett. 91(22), 224502 (2003)), coexisting with the basic flow, have been identified in the last few years. While they have been proved to play a certain role in the turbulent dynamics (B. Hof et al., Science 305, 1594 (2004)), their involvement in the transition process seems to be simply ungrounded. Furthermore, some recent experimental results point at a transitory nature of turbulence (B. Hof et al., Nature 443(7107), 59--62 (2006)), thus questioning the mere existence of a well defined critical threshold. The region of phase space dominated by turbulent dynamics would then be constituted by a surging amount of bifurcating complex solutions as the Reynolds Number is increased, acting as an attractor most of the time, but always retaining some probability that any trajectory finds its way back to laminarity. However transient may turbulence be, the notion of a threshold separating initial conditions that lead to transition from others that end up decaying still applies. It suffices to define the threshold as the point where the perturbation lifetime seems to diverge, possibly not to infinity if turbulence is a transient phenomenon, but still abruptly. Then, the threshold regains interest, and the question can be asked of how a solution wandering about criticality (T. Schneider et al., Phys. Rev. Lett. 99(3), 034502 (2007)) would look like. Starting from different initial conditions, and through accurate refinements, trajectories on the edge between turbulence and laminarity can then be analysed to elucidate which properties of a solution determine whether it belongs to the laminar or the turbulent basin of attraction. We analyse these trajectories to try and understand transition. Using an adapted Newton method we systematically search for travelling wave solutions underlying the dynamics of these critical trajectories.
HRTW01 10th September 2008
17:10 to 17:30
Subcritical instability in shear flows: the shape of the basin boundary
The boundary of the basin of attraction of the stable, laminar point is investigated for several of the dynamical systems modeling subcritical instability. In the cases thus far considered, this boundary contains a linearly unstable structure (equilibrium point or periodic orbit). The stable manifold of this unstable structure coincides at least locally with the basin boundary. The unstable structure plays a decisive role in mediating the transition in that transition orbits cluster tightly around its (one-dimensional) unstable manifold, illustrating a scenario proposed by Waleffe. The picture that emerges augments the bypass scenario for transition and reconciles it with Waleffe's scenario. We consider a model proposed by Waleffe (W97) for which an unstable equilibrium point U lies on the basin boundary. We find numerically that all orbits starting near U decay to the origin, whereas 'half' of them should remain permanently bounded away from the origin. We offer an interpretation of this tendency toward decay based on the structure of the basin boundary.
HRTW01 11th September 2008
09:40 to 10:00
Transition to turbulence in a pipe
The puzzle of why fluid motion along a pipe is observed to become turbulent as the flow rate is increased remains the outstanding challenge of hydrodynamic stability theory, despite more than a century of research. The issue is both of deep scientific and engineering interest since most pipe flows are turbulent in practice even at modest flow rates. All theoretical work indicates that the flow is linearly stable i.e. infinitesimal disturbances decay as they propagate along the pipe and the flow will remain laminar. Finite amplitude perturbations are responsible for triggering turbulence and these become more important as the non-dimensional flow rate, the Reynolds number Re, increases. Transition is generally abrupt and elucidating the details is difficult in practice. Here we report new experimental results on the appearance of periodic states which arise below the transition threshold. They are in accord with recent numerical results and their role in the transition process will be discussed.
HRTW01 11th September 2008
10:00 to 10:20
Highly-symmetric travelling waves in pipe flow
The recent theoretical discovery of finite-amplitude travelling waves in pipe flow has re-ignited interest in the transitional phenomena that Osborne Reynolds studied 125 years ago. Despite all being unstable, these waves are providing fresh insight into the flow dynamics. We describe two new classes of travelling wave which while possessing more restrictive symmetries than the previously found travelling waves of Faist & Eckhardt (2003) and Wedin & Kerswell (2004) seem to be more fundamental to the hierarchy of exact solutions. They exhibit much higher wall-shear stresses and appear at notably lower Reynolds numbers. The first M-class comprises of the various discrete-rotationally symmetric analogues of the mirror-symmetric wave found in Pringle & Kerswell (2007) and have a distinctive double layer structure of fast and slow streaks across the pipe radius. The second N-class has the more familiar separation of fast streaks to the exterior and slow streaks to the interior and looks like the precursor to the class of non-mirror-symmetric waves already known.
HRTW01 11th September 2008
10:20 to 10:40
Computational methods for finding exact solutions of shear flows
Direct numerical solution begins with an initial velocity field and uses the incompressible Navier-Stokes equation to evolve that field forward in time. It has been a huge success and has provided theoretical support for a large number of experiments and natural phenomena. To find steady solutions and traveling waves, one must solve for velocity fields that satisfy certain nonlinear requirements. To find periodic or relative periodic solutions, one must solve for an initial velocity field that evolves in time over a single period to reach a final state that is equal to the initial state modulo certain symmetries. This talk will describe the use of direct numerical solution, Krylov subspace methods, and the hookstep technique from nonlinear optimization to find such solutions.
HRTW01 11th September 2008
10:40 to 11:00
Transition to turbulence and turbulent bifurcation in a von Karman flow
We study the transition from laminar flow to fully developed turbulence in a von Karman flow (Re from 50 to 106). The flow undergoes a classical succession of bifurcations driven by the destabilization of the azimuthal shear-layer. We observe that the transition to turbulence is globally supercritical: the kinetic energy of the velocity fluctuations can be used as a single order parameter to characterize the transition. We also measure the dissipation through the torque injected in the flow. For high Reynolds numbers, the mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic Rπ-symmetry. The global bifurcation between these states is highly subcritical and the system thus keeps a memory of its history. The transition recalls low-dimension dynamical system transitions and exhibits slow dynamics and peculiar statistics. References F. Ravelet et al., J. Fluid Mech. 601, 339 (2008) F. Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)
HRTW01 11th September 2008
11:30 to 11:50
The role of coherent structures in low-Reynolds-number turbulent wall flows
Coherent states found numerically in plane Couette turbulence (Kawahara & Kida, J. Fluid Mech. 449, 2001; Kawahara, Phys. Fluids 17, 2005) and square duct turbulence (Uhlmann, Pinelli, Kawahara & Sekimoto, J. Fluid Mech. 588, 2007) are reviewed to discuss the role of coherent structures in wall-bounded turbulent flows at low Reynolds numbers. The coherent states in Couette flow are represented by unstable periodic solutions to the incompressible Navier-Stokes equation. The periodic solution, which exhibits a near-wall regeneration cycle of streamwise vortices and streaks, is shown to satisfy Prandtl's wall law, implying that the regeneration cycle has relevance to the statistical law of near-wall turbulent flow. The coherent states in marginally turbulent square duct flow are characterized by a four-vortex secondary flow and associated streaks. It is shown that at low Reynolds numbers streamwise vortices play a crucial role in the appearance of secondary flow of Prandtl's second kind.
HRTW01 11th September 2008
11:50 to 12:10
Statistics of passive vectors in an unstable periodic flow of Couette system
The statistics of orientation and location of passive vectors in an unstable periodic flow of Couette system are investigated numerically with special attention to the correlation with the coherent structures in the flow. The flow domain is divided into many small cubic regions and the distribution of directions of many passive vectors in each cube is calculated at several temporal phases of the unstable periodic flow. It is found that in most of cubes the passive vectors align either in a single direction (linear region) or on a plane (planar region). The unstable periodic flow exhibits the characteristic features of Couette turbulence having the streamwise vortices and the low-speed streaks. The linear regions are observed in streamwise vortices and low-speed streaks (or the ejection region near the wall), the planar regions in the periphery of vortices and in the sweep region near the wall. The dispersion in direction of passive vectors depends on their near-past history over the characteristic times of the unstable periodic flow.
HRTW01 11th September 2008
12:10 to 12:30
C Lee Transition in wall-bounded flows
In this article we present direct comparisons of experimental results on transition in wall-bounded flows obtained by flow visualizations, hot-film measurement, and particle-image velocimetry (PIV), along with a brief mention of relevant theoretical progresses, based on a critical review of about 120 selected publications. Despite somewhat different initial disturbance conditions used in experiments, the flow structures were found to be practically the same. The following observed flow structures are considered to be of fundamental importance in understanding transitional wall-bounded flows: The three-dimensional nonlinear wave packets called solitons-like coherent structures (SCS) in boundary layer and pipe flows; the ƒ©-vortex; the secondary vortex loops; and the chain of ring vortices. The dynamic processes of the formation of these structures and transition as newly discovered by recent experiments include, among others: (1) The sequential interaction processes between the ƒ©-vortex and the secondary vortex loops, which controls the manner by which the chain of ring vortices is periodically introduced from the wall region into the outer region of the boundary layerG (2) The generation of high-frequency vortices, which is one of the key issues for understanding both transitional and developed turbulent boundary layers (as well as other flows), of which several explanations have been proposed but a particularly clear interpretation can be provided by the experimental discovery of secondary vortex loops. The ignorance of secondary vortex loops would make the dynamic processes and flow structures in a transitional boundary layer inconsistent with previous discoveries; and (3) The dominant role of SCS in all turbulent bursting, which is considered as the key mechanism of turbulent production in a low Reynolds-number turbulent boundary layer. Of direct relevance to bursting is the low-speed streaks, whose formation mechanism and link to the flow structures in wall-bounded flows can be answered more clearly than before in terms of the SCS dynamics. We combine these newly observed structures and processes to those well-known ones to form a more integrated physical picture of the transitional dynamics. This not only enables revisiting the classic story of wall-bounded flow transition, but also opens a new avenue to reconstruct the possible universal scenario for wall bounded flow transition.
HRTW01 11th September 2008
14:00 to 14:20
The existence of very-large scale motions or superstructures' in wall-bounded turbulent flows
Recent experiments in the logarithmic and wake regions of wall-bounded turbulent flows have revealed the existence of very large-scale motions (with instantaneous length-scales up to 20 boundary layer thicknesses). This regime of very long meandering positive and negative streamwise velocity fluctuations (and associated roll-modes) appear to be universal features of all wall-bounded turbulent flows, having been recently documented in turbulent boundary layers, pipes, channels and atmospheric surface layers. Importantly, these structures appear to maintain a presence or footprint in the near-wall region, seeming to modulate or influence the near-wall cycle. As Reynolds number increases, not only is there an increase in scale-separation between these large-scale motions and the near-wall cycle, but also an increase in the overall energy of these long meandering features as compared to the viscous scales. This would seem to imply that these features will play an increasingly dominant role in high Reynolds number wall-bounded turbulent flows.
HRTW01 11th September 2008
14:20 to 14:40
Large scale structures of high Reynolds number turbulent boundary layers
Time-resolved measurements from the European Wallturb consortium experiment conducted using the large Laboratoire de Mecanique de Lille (LML) wind tunnel at Lille, France are reported. Data were taken at Re_theta = 9,800 and 19,100. Data were obtained using a rake of 143 single hot-wires which were spaced logarithmically across the flow in the spanwise and vertical directions over a distance approximately equal to the boundary layer thickness of 0.3 m. The wires were calibrated in situ using data from the simultaneous PIV experiment in a plane just upstream of the wire. Other PIV planes were also recorded in synch with the hot-wire data acquisition. This paper reports the cross-correlations and spectra generated among the wires themselves and those generated the upstream PIV plane immediately upstream of the rake. The existence of very long elongated structures are also shown by the space-time correlations obtained using the hot-wire rake data. Proper orthogonal decomposition (POD) applied on the same how-wire rake data are found to be very efficient in term of energy such that only a few spanwise wavenumber modes are necessary to capture 90% of the energy, and the details POD results like eigenspectra and eigenfunctions are discussed in the paper.
HRTW01 11th September 2008
14:40 to 15:00
Large scale features in turbulent pipe and channel flows
In recent years there has been significant progress made towards understanding t he large-scale structure of wall-bounded shear flows. Most of this work has been conducted with turbulent boundary layers leaving scope for further work in pipe s and channels. Here, the structure of fully-developed turbulent pipe and channel flow has been studied using custom-made arrays of hot-wire probes. R esults reveal long, meandering structures of length up to 25 pipe radii or chann el half-heights. These appear to be qualitatively similar to those reported in t he log region of a turbulent boundary layer. However, for the channel case, larg e-scale coherence persists further from the wall than in boundary layers. Further comparison of the three turbulent flows sh ows that the characteristic structure width in the logarithmic region of a bound ary layer is at least 1.6 times smaller than that in a pipe or channel.
HRTW01 11th September 2008
15:30 to 15:50
Large-scale motions in supersonic turbulent boundary layers
Wide-field and high-speed Particle Image Velocimetry measurements were performed in a Mach 2 supersonic turbulent boundary layer to characterise the structure of large-scale coherence. Instantaneous velocity fields in the logarithmic region reveal the presence of elongated uniform low- and high-speed regions. These elongated regions exhibit strong similarities with the large-scale motions found in incompressible boundary layers. Application of Taylor's hypothesis together with high-speed PIV data indicates that these large-scale structures could extend over 30-40 boundary layer thickness in length. Alternately, these can interpreted as 5-10 boundary layer thickness long structures lasting over several integral time scales. Regardless of interpretation, these elongated (spatio-temporal) structures appear to be play a significant role in the dynamics of shock-induced turbulent boundary layer separation. A possible mechanism that relates the passage of these elongated structures to the frequency of unsteadiness of shock-induced separation will be presented.
HRTW01 11th September 2008
15:50 to 16:10
An event-based description of the heat-flux time series in an atmospheric boundary layer
A new method of describing the turbulent momentum flux time series (which we call the ‘extended point-process’ method) has recently been proposed (Narasimha+ 2007 Phil. Trans A). In this method ‘flux events’ are identified in the associated time series, and their characteristics defined in terms of their contributions to the mean flux (so events can be of either sign). We extend the method here to provide a similar description of the eddy heat flux time series, and show the enormous influence exerted by the state of stability of the atmospheric boundary layer on flux-event statistics.
HRTW01 11th September 2008
16:10 to 16:30
A Gungor Multiscale simulation of wall-bounded flows
HRTW01 11th September 2008
16:50 to 17:10
J Klewicki On describing mean flow dynamics in wall turbulence
The study of wall-flow dynamics and their scaling behaviors with increasing Reynolds number warrants considerable attention. Attempts to date, however, have primarily focused on questions relating to what scaling behaviors occur, rather than the dynamical reasons why they occur. Given these considerations, the present talk is organized in three parts. In the first part it is shown that the predominant methodology for discerning the dominant mechanisms associated with the mean flow dynamics is problematic, and can lead to erroneous conclusions. In the second part we examine the Millikan-Izakson (inner/outer/overlap) arguments that underpin the widely accepted derivation for a logarithmic mean profile. Existing rigorous results from the theory of functions are outlined. They reveal that the Millikan-Izakson arguments constitute something very close to a tautology and embody little physics specific to turbulent wall-flows. The first two parts establish the context for the third. The presentation concludes with a physical interpretation of the mathematical conditions necessary for a logarithmic (or nearly logarithmic) mean profile. The basis for this interpretation is the analysis of Fife et al., (2005 JFM 532}, 165) which reveals that the mean differential statement of Newton’s second law rigorously admits a hierarchy of physical layers each having their own characteristic length. These analyses show that the condition for exact logarithmic dependence exists when the normalized equations of motion (normalized using the local characteristic length) attain a self-similar structure, and physically indicate that the leading coefficient in the logarithmic law (von Karman constant) will only be truly constant when an exact self-similar structure in the gradient of the turbulent force is attained across a range of layers of the hierarchy. These results are discussed relative to the physics of boundary layer Reynolds number dependence and recent data indicating that the von Karman constant varies for vary ing mean momentum balance.
HRTW01 11th September 2008
17:10 to 17:30
Inner-outer interaction in turbulent wall layers
A physical, but non-taxonomical, description of wall turbulence is presented. The requirements of self-similarity are discussed and, in particular, the effects of inner-outer interaction are explored. This interaction may be described as "bottom-up" (e.g. surface roughness) or "top-down" (e.g. high Reynolds number) and the consequences of each are discussed. It is shown that, while a weak interaction is, in fact, a statement of Townsend's ideas of ‘inactive’ motion, it is only a linear first approximation of a nonlinear process, which occurs primarily through the wall-normal component of velocity and the static pressure. It is shown that the interaction leads to a lack of similarity in terms of the structure and the second-order statistics. Using observations from a discrete wavelet analysis, a heuristic model of wall turbulence is described in which it is shown that the motion is driven by pressure-gradient fluctuations arising from the dominance of quasi-streamwise vortices. For linear control, the need for model reduction therefore suggests transient growth. Early results from measurements of roughness-induced transient growth in a Blasius base flow are described: issues concerning receptivity (to the initial disturbance) and observability are discussed. Some results from associated control experiments and simulations involving surface deformation are also presented.
HRTW01 12th September 2008
09:20 to 09:40
Slow temporal scales in the dynamics of vortices at large Reynolds numbers in a cylindrical experiment
We present results concerning an experimental setup where a fluid is stirred in a cylindrical cavity up to a Reynolds number of $10^6$. We show that the averaged velocity field of the turbulent flow bifurcates subcritically breaking some symmetries of the problem and becomes time-dependent because of equatorial vortices moving with a precession movement. This subcriticality produces a bistable regime, whose main characteristics are successfully reproduced using a three well potential model with additive noise. We characterized the hysteresis region, not previously observed, in this bifurcation. This hysteresis appears only for a extremely small range of parameters. Three different time-scales are relevant to the dynamics, two of them very slow compared to the impeller frequency.
HRTW01 12th September 2008
09:40 to 10:00
A Meseguer Subcritical equilibria in counter-rotating Taylor-Couette flow
We provide a numerical exploration of the spiral regimes that appear in small-gap Taylor-Couette flow of radius ratio 0.883 and for high counter-rotating Reynolds numbers. In particular, the exporation is carried out for a fixed outer rotation Reynolds number value of R_o=-1200. The spiral regimes found beyond the linear stability critical values are tracked back as a function of the inner rotation Reynolds number R_i with an arch-length continuation scheme via Newton-Krylov algorithms suitably tailored for axially-moving and/or azimuthally rotating reference frames. The spirals found have been found to be subcritical. This study is the first step taken in order to provide the essential inner structure of the skeleton of equilibria that may be responsible for the subcritical transition and hysteretic phenomena that has been reported by many experimentalists in the past.
HRTW01 12th September 2008
10:00 to 10:20
The sliding Couette flow problem
The sliding Couette flow, categorised by Joseph (1976), is a flow between concentric cylinders of radii, a and b ( > a), where the inner cylinder is pulled with an axial speed, U , relative to the stationary outer cylinder. It is known that the linear critical Reynolds number based on the speed U and the gap width, b-a, is infinite, at least when the radius ratio is not very small, so that secondary flows, if they exist, must bifurcate abruptly from the laminar state. The absence of linear instabilities occurs similarly in the problems, such as plane Couette flow, pipe Poiseuille flow and flow in a square duct, which have been extensively explored with success in recent years. As far as the author knows finite amplitude solutions in the sliding Couette flow have not yet been found. In this short paper we analyse both linear and nonlinear instabilities of the sliding Couette flow in the limit of narrow gap. Following Masuda, Fukuda & Nagata (2008) we apply a uniform rotation.O, in the streamwise direction in order to provoke rotational instabilities. The idea is to see whether bifurcated flows developed with increasing O may be sustained in the subcritical region and even exist as O is reduced back to zero. We show numerically that the critical Reynolds number approaches the global stability limit determined by energy theory in the limit of large rotation rate. A nonlinear analysis indicates that secondary flows bifurcating at a moderate rotation rate are characterized by three-dimensional spiral vortex structures. Attempted continuation of the secondary flow branch to the zero rotational rate will be discussed. References [1] Joseph,D. D. (1976) Stability of Fluid Motions I, Springer-Verlag. [2] Masuda, S., Fukuda, S. & Nagata, M. (2008) 'Instabilities of plane Poiseuille flow with a streamwise system rotation', J. Fluid Mech., 603, 189-206.
HRTW01 12th September 2008
10:20 to 10:40
Exact solutions in the 2-dimensional viscoelastic channel flow

Recently, it has been discovered that flows of polymer solutions can become unstable and exhibit turbulent-like behaviour at very small Reynolds numbers. As a rule, viscoelastic flows with curved streamlines are linearly unstable, while parallel shear flows are believed to exhibit a subcritical transition to a turbulent state. In the absence of inertia, these instabilities are driven by anisotropic elastic stresses.

Here I try to identify exact solutions in the 2D viscoelastic channel flow. Starting from the exact solutions of the Navier-Stokes equation found by Th. Herbert, solutions for the Oldroyd-B viscoelastic model are obtained by analytic continuation from the Newtonian case. It is found that these solutions persist at relatively small Reynolds numbers if the normal-stress difference is large enough. Nevertheless, so far I was unsuccessful in tracking these solutions down to the Re=0 limit. Other types of analytic continuation will be discussed as well.

HRTW01 12th September 2008
10:40 to 11:00
Stability in a plane channel flow with viscosity stratification
We discuss the stability of a channel flow with viscosity stratification. Three mechanisms of route to transition, namely linear, transient and secondary instability growths are investigated here. How does a viscosity-stratification alter the stability behaviour of these mechanisms in a channel flow? A temperature dependent viscosity is used obtain the viscosity gradients. It is concluded that all three routes to transition has different stability characteristics for any given kind of stratification. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Rayleigh-Benard and Poiseuille modes for Grashof numbers upto $\sim 25000$, which merge thereafter. We conclude that a knowledge of transition mechanism and type of stratification is necessary for viscosity variation to be exploited as an effective flow control mechanism.
HRTW01 12th September 2008
11:30 to 11:50
Lift-up and convective nonnormalities : the dynamics of a recirculation bubble
The stability of the recirculation bubble behind a smoothed backward-facing step is numerically computed. Destabilization occurs through a stationary three-dimensional mode. Analysis of the direct global mode shows that the instability corresponds to a deformation of the recirculation bubble in which streamwise vortices induce low and high speed streaks as in the classical lift-up mechanism. Formulation of the adjoint problem and computation of the adjoint global mode show that both the lift-up mechanism associated to the transport of the base flow by the perturbation and the convective nonnormality associated to the transport of the perturbation by the base flow explain the properties of the flow. The lift-up nonnormality differentiates the direct and adjoint modes by their component: the direct is dominated by the streamwise component and the adjoint by the cross-stream component. The convective nonnormality results in a different localization of the direct and adjoint global modes, respectively downstream and upstream. Implication of these properties on the linear and nonlinear dynamics will be discussed. co-workers: O. MARQUET, M. LOMBARDI , D. SIPP AND L. JACQUIN Departement d'Aerodynamique Fondamentale et Experimentale, ONERA, 92190 Meudon, France
HRTW01 12th September 2008
11:50 to 12:10
Global analysis of convective instabilities in nonparallel flows
A new scheme for the global analysis of convective instabilities in nonparallel flows is proposed. The linearized perturbation equations for an incompressible flow are written in a moving frame of reference that travels with the perturbation. In the moving frame, the base flow varies with time. However, at t=0, it is same as the one in stationary frame. Therefore, this analysis, for determining the global convective instability, is valid in an instantaneous sense. A stabilized finite element method is utilized to discretize these equations. A sub-space iteration procedure is utilized to solve the resulting generalized eigenvalue problem. Unlike local analysis, the proposed method gives the global eigenmode and the corresponding growth rate. The scheme is applied to assess the stability of uniform flow past bluff bodies. For the flow past a circular cylinder the critical Re for the onset of convective instability is found to be 4, approximately. The critical Re for the onset of the shear layer instability has been a point of contention. Various estimates have been proposed ranging from Re_c=350 to 2600. The proposed method is applied to find Re_c. To suppress the wake mode, that leads to Karman vortex shedding, flow past one half of the cylinder is studied. The Re_c is found to be ~54. The wake and shear layer modes for a full cylinder are compared to bring out the differences between the two. Also, the connection of the instability at low Re to the shear layer modes at higher Re (=500) is presented. The results are compared with earlier work from local stability analysis. Results are also computed for flow past a flat plate normal to the flow. All the results are in excellent agreement with the direct numerical simulation of the linearized flows equations.
HRTW01 12th September 2008
12:10 to 12:30
Bifurcation phenomena in the flow through a sudden expansion in a circular pipe
We report the results of an experimental investigation of laminar and time-dependent flows through a sudden expansion in a circular pipe. The flow state was investigated using high resolution MRI imaging techniques which have allowed us to settle a long standing debate on the first instability that occurs. As Re is increased, the flow passes through a steady symmetry breaking bifurcation such that the position of the recirculating eddy becomes asymmetric within the pipe. This in turn gives way to simple periodic motion via a Hopf bifurcation with further increase in Re.
HRTW01 12th September 2008
14:00 to 15:00
Summary and discussion
HRTW01 12th September 2008
15:30 to 16:20
Summary and discussion continued
HRT 15th September 2008
15:00 to 16:00
R Moser LES and modelling near-wall multipoint correlations
HRT 17th September 2008
15:00 to 16:00
Wall turbulence: from the laboratory to the atmosphere
The study of wall-bounded turbulent flows has received great attention over the past few years as a result of high Reynolds number experiments conducted in new high Reynolds number facilities such as the Princeton “Superpipe”, the NDF facility in Chicago and the HRNBLWT at the University of Melbourne. These experiments have brought into question the fundamental scaling laws of the turbulence and mean flow quantities as well as revealed high Reynolds number phenomena, which make extrapolation of low Reynolds number results highly questionable. In this talk these issues will be reviewed and new results from the HRNBLWT and atmospheric surface layer on the salt-flats of Utah will be presented documenting unique high Reynolds number phenomena. Modelling of these flows, using attached eddy hypothesis will also be discussed.
HRT 18th September 2008
15:00 to 16:00
Turbulent mixing regimes in stratified shear flow
HRT 22nd September 2008
15:00 to 16:00
A Lagrangian view of scalar transport and mixing
HRT 23rd September 2008
15:00 to 16:00
Instabilities of two-layer shallow-water flows with vertical shear in the rotating annulus
HRT 24th September 2008
15:00 to 16:00
Turbulence in four dimensions
HRTW05 26th September 2008
13:30 to 14:15
What are we going to need to keep computing turbulence, and what can we get in return
Direct numerical simulation has been one of the primary tools of turbulence research in the last two decades. Since the first simulations of low-Reynolds-number turbulent flows appeared in the early 1980's, the field has moved to higher Reynolds numbers and to more complex flows, until finally overlapping the lower range of laboratory experiments. This has provided a parametric continuity that can be used to calibrate experiments and simulations. It has turned out that, whenever both are available, simulations are usually the more consistent, mainly because they have essentially no instrumental constraints, and because the flow parameters can be controlled much more tightly than in the laboratory (although both are not necessarily equivalent). Perhaps more important is that simulations afford a degree of control over the definition of the physical system that is largely absent in the laboratory, allowing flows to be studied "piecemeal", and broken into individual "parts". We are now at the point in which these techniques can be applied to flows with nontrivial inertial cascades, thus providing insight into the "core" of the turbulence machinery. This has been made possible by the continued increase in computer power, which has roughly doubled every year, providing every decade a factor of 1000 in computing speed, and a factor of ten in Reynolds number. Software evolution has also been important, and will continue to be increasingly so. Numerical schemes have changed little, typically relying on high-resolution methods which require smaller grids, but hardware models have moved from vector, to cache-based to highly parallel, all of which have required major reprogrammings. Lately, most of the speed-up has come from higher processor counts and finer granularities, which interfere with the wide stencils of high-resolution methods. The trend towards complex flow geometries also pushes numerical schemes towards lower orders. This may bring at least a temporary slow-down in the rate of increase of Reynolds numbers. Moving from spectral to second-order methods typically requires a factor of three in resolution, or a factor of 80 in operation count. This is about six years of hardware growth. Another limiting factor is data storage and sharing. Typical simulations today generate Terabytes of data, which have to be archived, postprocessed, and shared with the community. This will increase to Petabytes shortly, especially if low-resolution grids are required. There are at present few archival high-availability methods for these data volumes, all of them expensive, and essentially no way to move the data among groups. Problems of this type have been common during the last two decades, and they have been solved. They will no doubt also be solved now, but they emphasise that simulations, although by now an indispensable tool of turbulence research, will continue to be far from routine for some time.
HRTW05 26th September 2008
14:15 to 15:00
Impacts and opportunities for leadership computing
Energy issues are central to the most important strategic challenges facing the United States and the world. The energy problem can be broadly defined as providing enough energy to support higher standards of living for a growing fraction of the world’s increasing population without creating intractable conflict over resources or causing irreparable harm to our environment. It is increasingly clear that even large-scale deployment of the best, currently-available, energy technologies will not be adequate to successfully tackle this problem. Substantial advances in the state of the art in energy generation, distribution, and end use are needed. It is also clear that a significant and sustained effort in basic and applied research and development (R&D) will be required to deliver these advances and ensure a desirable energy future. It is in this context that high-performance computing takes on a significance that is co-equal with theory and experiment. As computing enters the petascale, a capability that until recently was beyond imagination is now poised to address these critical problems. Oak Ridge National Laboratory is home to two supercomputer centers funded by the U.S. Department of Energy and the National Science Foundation. The world-leading petascale computers that are now being deployed will make it possible to solve R&D problems of importance to a secure energy future.
HRTW05 26th September 2008
15:20 to 16:05
A role of spectral turbulence simulations in developing HPC systems
Since the advent of supercomputers, numerical simulations for complicated phenomena have been made possible by applying their powerful computational capability. They gave it outstanding contributions to reveal the unknown in the wide variety of science and engineering fields, especially in turbulence. The spectral method has a large number of floating point operations in kernel loops and therefore requires high memory bandwidth between CPU and memory, as well as CPU performance. Moreover, since data transposition of 3-dimensional data array among parallel elements appears in parallel computation of the method, high bi-sectional bandwidth of inter-element network is also required. Therefore, it is the essential and important method to consider the HPC systems The recent trend of HPC systems which have more than ten thousand of parallel computational elements with low peak performance and low electricity, however, brings us some difficulties such as fine-grain parallelisation and low efficiency of computation in using HPC systems for the turbulence simulations. Longer simulation time will be requested if the systems have great peak performance like PFLOPS class. The trade-off between high performance capability and low electric power is essential issue in designing the HPC systems. We will discuss a possibility of higher resolution turbulence simulations by referring a recent trend of HPC systems and a development project of HPC system in Japan.
HRTW05 26th September 2008
16:05 to 16:50
Extreme scaling in turbulence simulations: challenges and opportunities for the research community
Current trends in developments towards Petascale computer hardware have pointed to the importance of developing algorithms in various fields of science capable of scaling up to extremely large numbers of parallel processing elements. We present performance benchmarking data for a turbulence simulation code based on a domain decomposition technique that allows the use of up to $N^2$ cores on $N^3$ periodic domain, with the largest test to date being at $N=8192$ on 32768 cores. While significant technical challenges remain in the path towards true Petascale performance in more complex geometries, we will discuss a range of opportunities for sharing both data and codes with the research community in order to maximize the scientific benefits of continuing rapid advances in computing power.
HRTW02 29th September 2008
10:00 to 10:30
Curvature of vortex tubes and sheets in turbulence
Weak structures of vorticity are studied as they evolve essentially passively as a result of the induced velocity field of the large-scale turbulence. Such objects are possibly an important component of the inertial and dissipation ranges of turbulence. Earlier work [1} along these lines concentrated on the effects of accumulated strain, apropos of Lagrangian chaos, on localized packets of vorticity. In particular it was shown that time-averaging the self-energy spectrum of such a structure leads to a fractional power law for the energy spectrum. In this paper we consider the effects of strain on the geometry of vortex tubes and sheets and concentrate on regions of high curvature, as an extension of other recent work [2]. In the case of a vortex tube, we find that a region of high curvature on the tube is likely to develop around a point where the vorticity vector is orthogonal to the principal axis of maximum strain. For vortex sheets, a region of high curvature is likely to occur where the above-mentioned principal axis is normal to the sheet. The strain tensor in question is that corresponding to the future deformation of a material element. We explore the notion that such high-curvature structures play a role in establishing the energy spectrum in inertial-range turbulence. References 1. A. Leonard 2002," Interaction of localized packets of vorticity with turbulence" in Proc. IUTAM Symp. on Tubes, Sheets, and Singularities in Fluid Dynamics (Kluwer) 201-210. 2. A. Leonard 2008, "The universal structure of high curvature regions of material lines in chaotic flows", submitted.
HRTW02 29th September 2008
10:30 to 11:00
Emerging symmetries and condensates in inverse cascades
I shall review symmetry aspects of turbulent inverse cascades in fluid mechanics, optics and plasma physics. Inverse cascades are generally scale invariant in distinction from most direct cascades. It has been recently discovered that in many cases scale scale invariance can be promoted to a more general and powerful conformal invariance. Namely, two-dimensional isolines of different fields (vorticity, temperature) belong to the remarkable class of curves called Schramm-Loewner evolution (SLE). I shall briefly review the properties of such curves. That discovery brings unexpected connections between fluid mechanics, mathematics (SLE was a subject of the recent Fields medal), theory of critical phenomena and quantum field theory. I then describe the appearance of spectral condensates (modes coherent across the whole system) due to inverse cascades. I briefly discuss the possible role of condensates in atmospheric physics, including the controversy on the energy flux at meso-scales. I shall describe initial findings on how condensates break symmetries established in inverse cascades.
HRTW02 29th September 2008
11:30 to 12:00
Kinetic theory representation for turbulence modeling and computation
One of the most common approximations in turbulence for the averaged effect of small scales is by the so called eddy viscosity modeling. That is, one approximates the Reynolds stress as a linear function of the local rate of strain of the averaged flow field. The proportionality constant is referred to as an eddy viscosity. This concept was first proposed over a century ago. It stems from an analogy for small eddy interactions with collisions of molecules resulting in Newtonian fluid constitutive relations. This approximation has made enormous impact particularly in computational fluid dynamics for turbulent flows. Many theoretical works were also developed since then, with various successes, in order to analytically derive such a functional relationship. However, unlike molecular interactions in a fluid, one of the apparent criticisms or difficulties in this analogy is the lack of scale separations between averaged fluid motions and fluctuating eddies. In this presentation, the speaker will give a somewhat provocative argument in favor of such analogy, provided that this concept be expanded in a generalized kinetic theory framework. In such an expanded framework, the analogy between eddy interactions and molecular collisions has a broader physical validity, while the eddy viscosity approximation is its consequence in the very long wave length limit. The kinetic theory representation itself needs not depend on scale separations. Using such an expanded analogy, one can also draw similarities between turbulent flow phenomena to that of non-Newtonian fluid flows in micro/nano scales. Nevertheless, other than phenomenological argument, as far as the speaker is aware, so far there have been little theoretical attempts to produce such a kinetic theory for turbulence on a concrete footing via first principle, if its physical soundness is acceptable.
HRTW02 29th September 2008
14:00 to 14:30
SV Nazarenko Bottleneck crossover between classical and quantum superfluid turbulence
We consider superfluid turbulence near absolute zero, which consists of a polarized tangle of mutually interacting vortex filaments with quantized vorticity. This system exhibits a classical K41-type cascade at the scales greater than the intervortex separation l, and Kelvin wave turbulence at the scales
HRTW02 29th September 2008
14:30 to 15:00
Homogeneous isotropic turbulence with polymer additives
We investigate the effects of polymer additives on flows that display homogeneous, isotropic turbulence by extensive direct numerical simulations (DNS) of (a) a shell model and (b) the Navier-Stokes equation coupled to an equation for the polymer-conformation tensor (the FENE-P model). Our simulations show that the addition of polymers to such flows leads to dissipation reduction in both decaying and statistically steady turbulence; this dissipation reduction is the analogue of drag reduction in wall-bounded flows. Our numerical results agree well with recent experimental results. In particular, we find that polymers decrease the energy of the turbulent fluid at intermediate length scales but increase it at small length scales; a scale-dependent viscosity provides a natural means of understanding our results. Preliminary studies of the multiscaling of structure functions, in the presence of polymer additives, and shock-capturing schemes for this problem are also discussed.
HRTW02 29th September 2008
15:30 to 16:00
Quantum turbulence -from superfluid helium to atomic Bose-Einstein condensates-
Quantum turbulence (QT) was discovered in superfluid in the 1950s, and the research has tended toward a new direction since the mid 90s. The similarities and differences between quantum and classical turbulence have become an important area of research in low temperature physics. QT is comprised of quantized vortices that are definite topological defects, being expected to yield a model of turbulence that is much simpler than the classical model. The general introduction of the issue is followed by a description of the dynamics of quantized vortices. After reviewing the modern research trends on QT, we focus on the energy spectrum of QT at very low temperatures. The numerical simulation of QT by the Gross-Pitaevskii model shows that energy is transferred through the Richardson cascade of quantized vortices and the spectrum obeys the Kolmogorov law. Then we discuss QT in trapped atomic Bose-Einstein condensates (BECs). Under the combined rotations around two axes, a BEC cloud develops to a turbulent state and the energy spectrum obeys the Kolmogorov law. Ref. M. Tsubota, cond-mat/ 08062737
HRTW02 29th September 2008
16:00 to 16:30
The spectrum of the vortex line density in a turbulent superfluid

Over the last twenty years, experiments and numerical simulations revealed strong similarities between Superfluid turbulence and Navier-Stokes turbulence. In particular, most measurements of integral quantities -such as the head loss in a pipe- or fluctuating ones -such as the velocity in the inertial range- could be interpretated by analogy with classical turbulence. Recently, measurements of the local fluctuations of the vortex lines density in superfluid 4He near 1.5 K have been reported. Over more than one decade of inertial range, the power spectrum was fitted with a f^(-5/3) power law. Remarkably, such a scaling differs from the one found in Navier-Stokes turbulence for the enstrophy, or for the absolute value of vorticity, which are often considered as classical counterparts of the vortex line density. We argue that this observation could be interpreted as the signature of a passive advection of the superfluid vortex lines by the largest scales of the flow.

Roche P.-E. & Barenghi C. , EPL 81: 36002 (2008)
http://crtbt.grenoble.cnrs.fr/helio/GROUP/infa.html

HRTW02 29th September 2008
17:00 to 18:00
Cryogenic turbulence
An overview of our knowledge of turbulence in both helium 4 and superfluid helium will be presented. The results will be cast in historical perspective and supplemented by numerical and theoretical ideas of the last fifty years.
HRTW02 30th September 2008
09:30 to 10:00
Anisotropic pressure and acceleration spectra in uniform shear flow
According to the local isotropic hypothesis, the small scale physical quantities such as velocity, temperature and pressure fluctuations are to be universal in any kind of turbulent flow. At this stage, the question is not whether this assumption is correct or not, but seems to be how the large scale anisotropy lost its information as the scale becomes small. In this talk, the anisotropic effect on inertial-range quantities are directly checked following the formula presented by Ishihara, Yoshida and Kaneda (P.R.L.,vol.88,154501,2002), in which the velocity correlation spectrum was uniquely determined by the rate of strain tensor of mean flow, the energy dissipation of per unit mass, and the two-non dimensional constants. This idea is applied to the pressure field in the uniform shear flow, and the shear effect on pressure and pressure gradient (acceleration) is studied experimentally up to the Reynolds number based on Taylor micro scale is 800. The results show the excellent agreement with the prediction by theory, and the universal trend of anisotropic spectra was observed.
HRTW02 30th September 2008
10:00 to 10:30
The standard multifractal cascade model assumes both a Markovian self-similar multiplicative cascade, and locality, in the sense that point properties depend only on their immediate neighbourhoods. Relaxing the second condition leads to more general cascades in which a point property v_{n+1} depends both on the local previous cascade step v_n, and on the global variance v'_n. The first contribution models a local breakdown process, while the second represents the effect of the background perturbations. There are two stochastic multipliers, one for each term, and they are characterised empirically for experimental high-Reynolds number experimental turbulence. General conditions are derived for such an imperfect multiplicative cascade to be intermittent, in the sense of creating unbounded high-order flatness factors after many steps. The experimental values are such as to be most likely intermittent, but they may not reach true multifractal distributions, and power laws for the structure functions, until extremely large Reynolds numbers.
HRTW02 30th September 2008
10:30 to 11:00
J Peinke New insights into turbulence
We present a more complete analysis of measurement data of fully developed, local isotropic turbulence by means of the estimations of Kramers- Moyal coefficients, which provide access to the joint probability density function of increments for n- scales \cite{JFM}. In this contribution we report on new findings based on this technique and based on the investigation of many different flow data over a big range of Re numbers.

In particular we show:

- An improved method to reconstruct from given data the underlying stochastic process in form of a Fokker-Planck equation, which includes intermittency effects, will be shown.

- It is shown that a new length scale, for turbulence can be defined, which corresponds to a memory effect in the cascade dynamics. This coherence length can be seen as analogue to the mean free path length of a Brownian Motion. For length scales larger than this coherence length the complexity of turbulence can be treated as a Markov process. We show that this Einstein- Markovian coherence length is closely related to the Taylor micro-scale.

- It is shown that the stochastic process of a cascade will change with the Re-number and its universal or non-universal behavior with changing large scale boundary conditions will be discussed.

- For longitudinal and transversal velocity increments we present the reconstruction of the two dimensional stochastic process equations, which shows that the cascade evolves differently for the longitudinal and transversal increments. A different "speed" of the cascade for these two components can explain the reported difference for these components. The rescaling symmetry is compatible with the Kolmogorov constants and the Karman equation and give new insight into the use of extended self similarity (ESS) for transverse increments.

- A method is presented which allows to reconstruct time series from a estimated stochastic process evolving in scale. The method itself is based on the joint probability density which can be extracted directly from given data, thus no estimation of parameters is necessary. The original and reconstructed time series coincide with respect to the unconditional and conditional probability densities. Therefore the method proposed here is able to generate artificial time series with correct n-point statistics.

HRTW02 30th September 2008
11:30 to 12:00
On extension of the formalism MPDFA and its application to the analyses of DNS 4096$^3$ conducted by Kaneda and Ishihara
Our original theoretical framework, named Multi-fractal Probability Density Function Analysis (MPDFA), has been extended successfully in order to make it possible to analyze a series of probability density functions (PDFs), extracted from experiments and numerical simulations, with arbitrarily changed measuring areas or distances for various physical quantities representing intermittent behavior characterizing fully developed turbulence.

MPDFA is a unified self-consistent approach for the systems with large deviations, which has been constructed based on the Tsallis-type distribution function following the assumption raised by Frisch and Parisi that the singularities due to the scale invariance of the Navier-Stokes equation for high Reynolds number distribute themselves multifractal way in real physical space. MPDFA can be said as a generalization of the log-normal model. It was shown that MPDFA derives the log-normal model when one starts with the Boltzmann-Gibbs distribution function instead of Tsallis-type distribution function.

As a test of the validity of the extension, we analyzed the PDFs for energy transfer rates and for energy dissipation rates extracted by Kaneda and Ishihara group at Nagoya University from their DNS 4096$^3$.

In this talk, we will present mainly on the theoretical extension of MPDFA and its validity. The detailed analyses of PDFs out of DNS 4096$^3$ and the physical outcomes from them will be given at our poster presentation of this workshop.

• http://www.px.tsukuba.ac.jp/home/tcm/arimitsu/Marseilles04.pdf - Journal of Physics: Conference Series {\bf 7} (2005) 101--120.
• http://www.px.tsukuba.ac.jp/home/tcm/arimitsu/Roman%202.pdf - Anomalous Fluctuation Phenomena in Complex Systems: Plasma Physics, Bio-Science and Econophysics (Special Review Book for Research Signpost), eds. C.~Riccardi and H.E.~Roman (Transworld Research Network, Kerala, India, 2008) in press.
HRTW02 30th September 2008
12:00 to 12:30
The structure of the velocity and passive scalar mixing in a multiple opposed jets reactor
We document an experimental investigation of a confined chamber in which fluid is injected through two sets of 16 opposed jets that issue from top/bottom boundary porous planes. The investigated Reynolds numbers, based on injection velocity and jet diameter are up to 28,000. The high Reynolds numbers and impinging configuration of the flow produce very intense turbulence levels and a turbulence with zero mean velocity in the central region of the reactor. The analysis is done for basically two geometries: opposed jets with strong backflow, and opposed jets with very slow backflow. Particles Image Velocimetry (PIV) measurements in different planes allowed for a characterization of the mean and fluctuating velocity fields. Fluid recirculation in the reactor creates annular shear layers. The central region of the reactor includes stagnation regions, where mean vertical velocity gradients are very strong with low local mean velocity values, leading to high rms-to-mean velocity ratios. Such gradients are responsible for considerable kinetic-energy production, that sharply peaks in the central region. A particular attention is paid to the determination of the small-scales characteristics (energy dissipation rate) in different points of the flow, which is done using both PIV (using indirect methods, i.e. inertial-range information) and LDV (Laser Doppler Anemometry). Inertial-range behaviour is discussed, in terms of second and third-order structure functions, and a critical comparison with classical (forced) flows is done.

A passive scalar (Sc=1.3) is injected in the flow, in an alternate sequence (Z=0 and Z=1) among each two opposed jets and measured using Laser-Induced Fluorescence. Scalar structure functions are investigated, as well as the extent to which isotropy and homogeneity are adequate approximations for this flow. Flow visualisations exhibit very sharp scalar gradients at the frontier among two opposed jets. The dynamics of these regions closely follows that dictated by the back-and-forth motion developed in the central region, due to the opposed jets instabilities. Thus, the scalar is directly injected at the level of small scales, whereas the velocity field itself is injected over a whole range of scales. This directly leads to a very effective mixing in the stagnation region of the opposed jets.

HRTW02 30th September 2008
14:00 to 14:30
J Schumacher Statistics and growth rates of high-amplitude vorticity events in turbulence
Fluid turbulence is often characterized as a tangle of many intermittent vortices embedded in regions of straining motion. Although there have been many experimental and numerical studies on the evolution of isolated intense vortices, pairs of them or on the kinematics of ensembles of randomly distributed vortices, not much is known about their dynamic evolution in a fully turbulent flow. We present a high-resolution numerical simulation that monitors the formation and time evolution of high-amplitude vorticity regions. In order to identify and follow these events, we track the turbulence fields in local Cartesian frames of reference which move with Lagrangian tracers through the fluid. The local enstrophy -a measure of vorticity- shows temporal growth compatible on average with a classical prediction by Howarth and von Karman (1938). It remains well below a recently predicted rigorous upper bound for the enstrophy growth (Lu and Doering, 2008). However locally, enstrophy growth rates are detected that go beyond the mean trend and approach the predicted global bound. Related Links * http://www.tu-ilmenau.de/tsm - Homepage of Theoretical Fluid Mechanics Group
HRTW02 30th September 2008
14:30 to 15:00
T Ishihara Statistics of two-point velocity difference in high-resolution direct numerical simulations of turbulence in a periodic box
Statistics of two-point velocity difference are studied by analyzing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to $4096^3$ grid points. The DNS consist of two series of runs; one is with $k_{max}\eta\sim 1$ (Series 1) and the other is with $k_{max}\eta\sim 2$ (Series 2), where $k_{max}$ is the maximum wavenumber and $\eta$ the Kolmogorov length scale. The maximum, time-averaged, Taylor-microscale Reynolds number $R_\lambda$ in Series 1 is about 1145, and it is about 680 in Series 2. Particular attention is paid to the possible Reynolds number ($Re$) and $r$ dependence of the statistics, where $r$ is the distance between two points. The statistics include the probability distribution functions (PDFs) of velocity differences and the longitudinal and transversal structure functions. DNS data suggest that the PDFs of the longitudinal velocity difference at different values of Re but the same values of $r/L$, where $L$ is the integral length scale, overlap well with each other when r is in the inertial subrange and when using the same method of forcing at large scales. The similar is also the case for the transversal velocity difference. The tails of the PDFs of normalized velocity differences ($X$'s) are well approximated by such a function as $\exp(-A|X|^a)$, where $a$ and $A$ depend on $r$, and where $a$ becomes $\approx 1$ in the inertial subrange. Analysis shows that the scaling exponents of the $n$th-order longitudinal and transversal structure functions are not sensitive to $Re$ but sensitive to the large-scale anisotropy and non-stationarity, and suggests that nevertheless their difference is a decreasing function of $Re$.
HRTW02 30th September 2008
15:30 to 16:00
CVS filtering to study turbulent mixing
Coherent Vortex Simulation (CVS) is based on the wavelet filtered Navier-Stokes equations, where at each instant the turbulent flow is split into two orthogonal contributions: the coherent flow made of vortices which is kept, and the incoherent flow made of the background fluctuations which is discarded. The CVS filter is based on an orthogonal wavelet decomposition of the vorticity field where only the wavelet coefficients whose modulus is larger than a given threshold are kept. The value of the threshold depends only on the total enstrophy and on the numerical resolution used to represent the flow. The CVS filter has already been applied to 2D [Farge, Schneider and Kevlahan in Phys. Fluids 11(8) 1999] and 3D [Farge, Pellegrino and Schneider in Phys. Rev. Lett. 87(55) 2001, Farge et al. in Phys. Fluids 15(10) 2003, Okamoto et al. in Phys. Fluids 19 2007] turbulent flows, where it has been shown that only few wavelet coefficients (from 0.7% for 256^2 up to 2.6% for 2046^3 resolution) are sufficient to represent the coherent flow which preserves the vorticity and velocity PDFs, the energy spectrum and the nonlinear transfers all along the inertial range. We will analyze the time evolution of a decaying homogeneous isotropic turbulent flow, by applying the CVS filter at each time step of a Direct Numerical Simulation (DNS). We will compare the Eulerian and Lagrangian mixing properties of the total, coherent and incoherent flows by studying how they advect a passive tracer and many particles during several eddy turn-over times. We will quantify the mixing properties of coherent and incoherent flows and show that efficient mixing is due to the transport by vortices, while the incoherent contribution is much weaker and only diffusive. Related Links * http://wavelets.ens.fr - Web
HRTW02 30th September 2008
16:00 to 16:30
Energy cascade in turbulent flows: quantifying effects of Reynolds number and local and nonlocal interactions
The classical Kolmogorov theory of three-dimensional turbulence is based on the concept of the energy transfer from larger to progressively smaller scales of motion. The theory postulates that bulk of the energy transfer in the inertial range of turbulence occurs between scales of similar size, a process known as the local energy cascade. The locality allows to postulate that after multiple cascade steps the small scale dynamics become universal, i.e., independent of particulars of large scales that are determined by geometry, boundary conditions, and forces causing a flow. Yet despite its central role in the Kolmogorov theory the locality assumption cannot be easily verified, neither analytically nor experimentally. This is because the energy transfer is a result of interactions among different scales of motion originating from the nonlinear term in the Navier-Stokes equation that couples all scales. Relevant questions have been productively addressed for the first time using databases generated in large scale numerical simulations. We revisit and extend previous work and use such databases to compute detailed energy exchanges between scales of motion obtained by decomposing numerical velocity fields using banded filters, and investigate how the detailed transfers contribute to the global quantities such as the classical energy transfer, the energy flux, and the subgrid-scale transfer. We address two questions in detail. First, for the purposes of quantitative analyzes, various definitions of scales of motion can be used. This non-uniqueness leads to the possibility, raised in the literature on the subject, that properties of the energy transfer deduced from such analyzes can be qualitatively affected by the employed scale definitions. We address this question by computing detailed energy exchanges between different scales of motion defined by decomposing velocity fields using three specific filters: sharp spectral, Gaussian, and tangent hyperbolic. Second, we quantify the locality of the energy transfer and address a persistent controversy concerning the role of nonlocal interactions in the energy transfer process, i.e., the role of much larger scales than those transferring energy. The analysis of detailed interactions reveals that the individual nonlocal contributions are always large but significant cancellations lead to the global quantities asymptotically dominated by the local interactions. The detailed locality functions are computed and their behavior compared with the asymptotic scaling laws valid for infinite Reynolds numbers turbulence. Apart from an intellectual challenge of clarifying these issues, obtained results have bearing on practical questions of turbulence modeling that will also be addressed in the talk.
HRTW02 30th September 2008
16:30 to 17:00
Physical-space decimation and constrained large Eddy simulation
Traditional decimation theory of fluid turbulence was proposed by Kraichnan and the analysis was carried out in the Fourier space. It has been shown that the low-order decimation theory leads to the direct-interaction-approximation, while the high-order decimation theory can include the effect of intermittency. In this talk, we propose a physical-space decimation method which can be used for large-eddy-simulation. In particular, we propose to impose physical constraints in the dynamic procedure of the dynamic subgrid-scale (SGS) stress model in large eddy simulation, and to calculate the SGS model coefficients using a constrained variation. One simple constraint for fluid turbulence in both physical and Fourier space decimation models is the conservation of energy across the inertial range. Numerical simulations of forced and decaying isotropic turbulence demonstrate that the constrained dynamic mixed model predicts the energy evolution and the SGS energy dissipation well. The constrained SGS model also shows a strong correlation with the real stress and is able to capture the energy backscatter, manifesting a desirable feature of combining the advantages of dynamics Smagorinsky and mixed models. It should be mentioned that all previous LES models do not satisfy underlying physical constraints. We have also extended the constrained LES to helical, passive-scalar and intermittent systems.
HRTW02 30th September 2008
17:10 to 17:40
Extraction of the hierarchical energy spectrum in forced turbulence
Properties of the energy spectrum in turbulent flows are studied using the DNS data for forced homogeneous isotropic and shear turbulence. The perturbation expansion about the Kolmogorov -5/3 energy spectrum yields the hierarchical spectrum, in which the -7/3 spectrum induced by the fluctuation of the dissipation rate is added. Averaging conditioned on the temporal variations of dissipation rate is applied to the ensemble of the energy spectra. The base steady spectrum fits -5/3 power, but its deviatoric part exhibits a fitting with -7/3 power. The role of the -7/3 power spectrum in generation of energy cascade is elucidated by examining the temporal variations of the energy spectrum and transfer function. The cascade process is divided into two phases. The energy contained in the low-wavenumber range in Phase 1 is transferred to the high wavenumbers in Phase 2 with switchover of the sign in the -7/3 power component. In Phase 1, a very large gain in the energy transfer function occurs at the scale corresponding to the integral length. The vortex sheet whose lateral length is comparable to the scale of this input is created, and many Mode 3 or 2 spiral vortices (LSV) (Horiuti & Fujisawa 2008) are detected in Phase 1. These LSVs are converted to Mode 1 in Phase 2. The statistics are compared in Phases 1 and 2. The turbulent energy is larger in Phase 1 than in Phase 2. The moderately large dissipation rate dominates in Phase 2, but the dissipation field is more intermittent in Phase 1. Averaging conditioned on the dissipation and enstrophy indicates that the regions of extreme dissipation and enstrophy possess a significant degree of overlap in space in Phase 1. These extreme events occur along the spiral sheet of Mode 3 LSV which is strained and stretched by the tube in the core.
HRTW02 30th September 2008
17:40 to 18:00
Y Li Lagrangian evolution of non-Gaussianity and material deformation in restricted Euler dynamics
Small-scale intermittency in fluid turbulence refers to the infrequent but strong bursts in the signals of small scale parameters. These bursts display highly non-Gaussian statistics, and its prediction poses serious challenges to turbulence research. Based on the restricted Euler approximation, and following the recent idea of tetrad dynamics, we derive a simple system of equations for the short-time Lagrangian evolution of velocity and passive scalar increments. The system reproduces several important intermittency trends observed in turbulence. A generalization to rotating turbulence shows that system captures some qualitative effects of rotation. An analytic solution to the material deformation in restricted Euler dynamics, obtained following the same idea, is also presented.
HRTW02 1st October 2008
09:00 to 09:30
On the large-scale structure of two-dimensional turbulence
We consider freely-decaying, two-dimensional, isotropic turbulence. It is usually assumed that, in such turbulence, the energy spectrum at small wavenumber, k, takes the form E(k->0)=Ik^3 , where I is the two-dimensional version of Loitsyansky’s integral. However, a second possibility is E(k->0)=Lk , where the pre-factor, L, is the two-dimensional analogue of Saffman’s integral. We show that, as in three dimensions, L is an invariant and that E~Lk spectra arise whenever the eddies possess a significant amount of linear impulse. The conservation of L is shown to be a direct consequence of the principle of conservation of linear momentum. We also show that isotropic turbulence dominated by a cloud of randomly located monopole vortices has a singular energy spectrum of the form E(k->0)=Jk^-1, where J, like L, is an invariant. However, while E~Jk^-1 necessarily implies the existence of a sea of monopoles, the converse need not be true: a sea of monopoles whose spatial locations are not entirely random, but constrained in some way, need not give a E~Jk^-1 spectra. The constraint imposed by the conservation of energy is particularly important,ruling out E~Jk^-1 spectra for certain classes of initial conditions. We illustrate these ideas with some direct numerical simulations.
HRTW02 1st October 2008
09:30 to 10:00
Resolving the cascade bottleneck in vortex-line turbulence
Both in many superfluid experimental situations and simulations of a 3D hard-core interaction model, it is found that the vortex line length in superfluid turbulence decays in a manner consistent with classical turbulence. Two decay mechanisms have been proposed, Kelvin wave emission along lines and phonon radiation at small scales. It has been suggested that both would require a Kelvin wave cascade, which theory says cannot reach the smallest scales due to a bottleneck. In this presentation we will discuss a new approach using a recent quaterionic formulation of the Euler equations, coupled with the local induction approximation. Without the extra quaterionic terms It can be shown that if there are sharp reconnections, the above scenario occurs. But with the extra terms, the direction of propagation of nonlinear waves is reversed, there is a cascade to the smallest scales that could create phonons, and the paradox can be resolved.
HRTW02 1st October 2008
10:00 to 10:30
The absence of bottleneck in the Lagrangian-averaged model for incompressible magnetohydrodynamics
In order to better understand the small scale dynamics of geophysical and astrophysical flows with huge Reynolds numbers, numerical modeling is an invaluable tool but it needs to be assessed against experimental and observational data as well as direct numerical simulations (DNS) at high resolution. In this context, we study the properties of the Lagrangian-averaged magnetohydrodynamics (MHD) $\alpha-$model, LAMHD hereafter; this model can be viewed as a norm-preserving filtering of the primitive MHD equations. Among its advantages is the fact that the LAMHD formulation preserves the basic properties of MHD, e.g. the Alfv\'en theorem of flux conservation, and invariants such as the total energy, the cross-correlation between the velocity and magnetic field and magnetic helicity, albeit in a modified (H_1) form. LAMHD has been tested in two and three space dimensions and is found to behave satisfactorily, for example reproducing the threshold for dynamo action at moderately low magnetic Prandtl numbers P_M, as encountered in the liquid core of the Earth, the solar convection zone or in liquid metals in the laboratory (where P_M is the ratio of viscosity to magnetic diffusivity). Here we demonstrate that, for the case when there is initially quasi-equipartition between the velocity and the magnetic field and with a magnetic Prandtl number equal to unity, the model reproduces well both the large-scale and small-scale properties of turbulent flows; in particular, it displays no increased (super-filter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the sub-filter-scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes $\alpha-$model is somewhat more limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of super-filter-scale spectral properties. The LAMHD model is thus shown to be capable of leading to large reductions in required numerical degrees of freedom for a given set of kinetic and magnetic Reynolds number. Specifically, we find a reduction factor of approx 200 when compared to a direct numerical simulation on a large grid of 1536^3 points at the same Taylor Reynolds number approx 1700. The DNS having been stopped at the peak of dissipation of total energy, the run was pursued using LAMHD. We thus also report on preliminary explorations of the decaying dynamics of that high Reynolds number MHD flow at late times using the LAMHD model.
HRTW02 1st October 2008
10:30 to 11:00
Kinetic turbulence: a nonlinear route to dissipation through phase space
This talk will describe a conceptual framework for understanding kinetic plasma turbulence as a generalized form of energy cascade in phase space. It is emphasized that conversion of turbulent energy into thermodynamic heat is only achievable in the presence of some (possibly arbitrarily small) degree of collisionality. The smallness of the collision rate is compensated by the emergence of small-scale structure in the velocity space. For gyrokinetic turbulence, a nonlinear perpendicular phase mixing mechanism is identified and described as a turbulent cascade of entropy fluctuations simultaneously occurring in the gyrocentre space and in velocity space. Scaling relations for the corresponding fluctuation spectra are derived. An estimate for the collisional cutoff is provided. The relevance of these results to understanding the dissipation-range turbulence in the solar wind and the electrostatic microturbulence in fusion plasmas is discussed. Related Links * http://arxiv.org/abs/0806.1069 - preprint
HRTW02 1st October 2008
11:30 to 11:50
On enstrophy dissipation in 2D turbulence
We consider dissipation of enstrophy, one half the integral of squared vorticity, in 2D incompressible, turbulent flows at very high Reynolds number. We prove rigorously that, if fully developed turbulence is to be modeled mathematically by irregular (weak) solutions of the 2D Euler equations in the limit of vanishing viscosity, then there is no dissipation as long as the initial enstrophy is finite. We also provide examples of dissipative flows when the initial enstrophy is infinite. Our analysis is inspired by work of G. Eyink. This is joint work with Helena and Milton Lopes.
HRTW02 1st October 2008
11:50 to 12:10
Thresholds for the formation of satellites in two--dimensional vortices
We examine the evolution of a two--dimensional vortex which initially consists of an axisymmetric monopole vortex with a perturbation of azimuthal wavenumber m=2 added to it. If the perturbation is weak then the vortex returns to an axisymmetric state and the non--zero Fourier harmonics generated by the perturbation decay to zero. However, if a finite perturbation threshold is exceeded, then a persistent nonlinear vortex structure is formed. This structure consists of a coherent vortex core with two satellites rotating around it.

We consider the formation of these satellites by taking an asymptotic limit in which a compact vortex is surrounded by a weak skirt of vorticity. The resulting equations match the behaviour of a normal mode riding on the vortex with the evolution of fine--scale vorticity in a critical layer inside the skirt. Three estimates of inviscid thresholds for the formation of satellites are computed and compared: two estimates use qualitative diagnostics, the appearance of an inflection point or neutral mode in the mean profile. The other is determined quantitatively by solving the normal mode/critical--layer equations numerically. These calculations are supported by simulations of the full Navier--Stokes equations using a family of profiles based on the tanh function.

HRTW02 1st October 2008
12:10 to 12:30
MD Bustamante Capturing reconnection in Navier-Stokes and resistive MHD dynamics
In this work, the phenomena of vortex reconnection in Navier-Stokes (and magnetic reconnection in MHD), of importance in fully developed turbulence, are studied from the point of view of the Eulerian-Lagrangian representation. This representation is interpreted as a full characterization of fluid motion using only particle description. New generalized equations of motion for the Weber-Clebsch potentials associated to this representation are derived. We perform direct numerical simulations in order to confirm the validity of the paradigm proposed by Constantin where particles will diffuse anomalously in the space -and time- vicinity of reconnection events. For Navier-Stokes, the generalized formalism captures the intense reconnection of vortices of the Boratav, Pelz and Zabusky flow, in agreement with the previous study by Ohkitani and Constantin. For MHD, the new formalism is used to detect magnetic reconnection in several flows: the 3D Arnold, Beltrami and Childress (ABC) flow and the (2D and 3D) Orszag-Tang vortex. It is concluded that periods of intense activity in the magnetic enstrophy are correlated with periods of increasingly frequent resettings. Finally, the positive correlation between the sharpness of the increase in resetting frequency and the spatial localization of the reconnection region is discussed. Related Links * http://arxiv.org/abs/0804.3602v1 - ArXiv Preprint of Paper
HRTW02 1st October 2008
14:00 to 14:30
JC Vassilicos Non-universality of the turbulence dissipation constant in homogeneous isotropic turbulence and the universal relations which account for it
The dimensionless dissipation constant of homogeneous isotropic turbulence is equal to the third power of a number which reflects the number of large-scale eddies multiplied by a function of Reynolds number. This function of Reynolds number may tend to a constant in the limit of very high Reynolds number as a result of an eventual balance between a slow growth of the range of viscous length-scales and the increasing non-Gaussianity of the small scales. However, when the turbulence is generated by fractal grids this function of Reynolds number is inversely proportional to the Reynolds number for a very wide range of Taylor length-based Reynolds number up to about 1000 even though the turbulence energy spectrum has a well-defined -5/3 range. See Mazellier, N. & Vassilicos, J.C. 2008 The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology. Phys. Fluids 20, 015101 Seoud, R.E. & Vassilicos, J.C. 2007 Dissipation and decay of fractal-generated turbulence. Phys. Fluid 19, 105108
HRTW02 1st October 2008
14:30 to 15:00
M Oberlack Scaling law of fractal-generated turbulence and its derivation from a new scaling group of the multi-point correlation equation
Investigating the multi-point correlation equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with the Euler or Navier-Stokes equations from which the multi-point correlation equations have orginally emerged. This was first observed for parallel wall-bounded shear flows (see Khujadze, Oberlack 1994, TCFD (18)) though there this property only holds true for the two-point equation. Hence, in a strict sense there it is broken for higher order correlation equations. Presently using this extended set of symmetry groups a much wider class of invariant solutions or turbulent scaling laws is derived for homogeneous turbulence. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see Vassilicos etal.) fall into this new class of solutions. This is in particular a constant integral and Taylor length scale downstream of the fractal grid and the exponential decay of the turbulent kinetic energy along the same axis. These particular properties can only be conceived from multi-point equations using the new scaling symmetry since the two classical scaling groups of space and time are broken for this specific case. Hence, extended statistical scaling properties going beyond the Euler and Navier-Stokes have been clearly observed in experiments for the first time.
HRTW02 1st October 2008
15:30 to 16:00
How deep should one go to get the inertial range right?
Theoretical and empirical arguments will be presented to show that the grid resolution in direct numerical simulations ought to be finer than previously thought. Error estimates for poorer resolutions will be presented. By going deep in the dissipation region, it may be possible to recover inertial range properties at finite Reynolds numbers.
HRTW02 1st October 2008
16:00 to 16:30
Kolmogorov 4/5 law, nonlocality and sweeping decorrelation hypothesis
Results of experiments at high Reynolds numbers - both field an airborne - are used to validate an equivalent form of the 4/5 Kolmogorov, which demonstrate one of important aspects of non-locality of turbulent flows in the inertial range and stand in contradiction with the sweeping decorrelation hypothesis understood as statistical independence between large and small scales. This is supported by a set of exact purely kinematic relations also validated experimentally.
HRTW02 1st October 2008
16:30 to 17:00
T Tatsumi Statistical mechanics of fluid turbulence based on the cross-independence closure hypothesis
Statistical theory of turbulence is presented, which deals with homogeneous isotropic turbulence and inhomogeneous turbulent flows, their large-scale structures and small-scale similarities on an equal footing, using the "cross-independence closure hypothesis" proposed by Tatsumi(2001) for closing the Lundgren-Monin equations(1967) for the multi-point velocity distributions. Homogeneous isotropic turbulence at large Reynolds numbers is shown to be governed by the closed set of the one- and two-point velocity distributions. The distributions are expressed as the universal inertial-normal distributions associated with their own energy-dissipation rates as only parameters. Only exception from this universality is the longitudinal velocity-difference distribution, which is given by the local non-normal distributions in the inertial and viscous subranges. These theoretical results are discussed in comparison with the existing experimental and numerical results. Inhomogeneous turbulent flows at large Reynolds numbers are shown to be governed by the closed set of equations for the mean velocity and the one- and two-point velocity distributions. These equations have eminent feature that the effect of the mean flow is limited to the lage-scale components of turbulence. This feature is expected to largely simplify the formalism of shear-flow turbulence just like the 'boundary layer' in laminar flows.
HRTW02 1st October 2008
17:10 to 17:40
Modelling two-time velocity correlations for prediction of both Lagrangian and Eulerian statistics
More information on two-point two-time velocity correlations are needed for a better prediction of turbulent dispersion as well as radiated noise using an acoustic analogy. Conceptual aspects will be emphasized and not applications. Only isotropic turbulence will be considered, although many applications are developped in our team towards strongly anisotropic turbulence, mainly in rotating, stably stratified and/or MHD flows.

A simple synthetic model of isotropic turbulence is firstly considered, using a random superposition of Fourier modes : This is the KS (Kinematic simulation) following Kraichnan and Fung et al. Unsteadiness of velocity field realizations is mimicked using temporal frequencies, which are expressed in term of a prescribed energy spectrum and the wavenumber. Even if the orientation of the wavevector is randomly chosen, the link of the temporal frequency to the wavenumber is deterministic in the simpler version of the KS model. Although such a model was relevant for several applications, it is dramatically questioned for the evaluation of two-time velocity correlations. It is shown that spurious oscillations are generated, and that it is needed to model the temporal frequencies as random Gaussian variables with a standard deviation of the same order of magnitude as their mean value. Further applications to noise radiation are touched upon, in order to illustrate dominant (Lagrangian) straining' or dominant (Eulerian) sweeping' effects, according to the scale under consideration.

The role of a typical time-scale for the decorrelation of triple velocity correlations is then recalled and discussed in the classical triadic closures' from the Orszag and Kraichnan's legacy, such as EDQNM, DIA and semi-Lagrangian more sophisticated variants.

Finally, these different concepts (diffusive and/or dispersive eddy dampings, straining or sweeping processes) are applied to a recent closure theory of weakly compressible isotropic turbulence. A Gaussian kernel for the decorrelation of triple velocity correlations was shown to give much better results than the classical exponential kernel inherited from EDQNM in the incompressible case. A new explanation is given in accordance with the renormalization of the acoustic wave frequency by a pure random term with zero mean but with a standard deviation of the same order of the eddy damping term formerly used in EDQNM. This analysis can be related to the concept of Kraichnan's random oscillator, recently revisited by Kaneda (2007), with a connection to the much simpler KS problem firstly presented (see also the monograph homogeneous turbulence dynamics' by Pierre Sagaut and Claude Cambon, just published in Cambridge University Press.)

HRTW02 2nd October 2008
09:00 to 09:30
Lagrangian velocity statistics in turbulence: theory, experiments and numerics
A detailed comparison between experimental and numerical data of Lagrangian velocity structure functions in turbulent flows is presented. Thanks to the integration of information coming from experimental and numerical data, a quantitative understanding of the velocity scaling properties over a wide range of time scales and Reynolds numbers can be achieved. Intermittency changes if measured close to the Kolmogorov time scales or at larger time lags. A quantitative comparison with prediction from multifractal theory for Lagrangian turbulence will also be presented. These results shed some new insight on the relevance of vortex filaments for the statistics of tracers and/or heavy/light particles in turbulence.
HRTW02 2nd October 2008
09:30 to 10:00
Experimental results on the dynamics of tracers and inertial particles in highly turbulent flows
We report measurements on the statistics of two particle dispersion, acceleration, and velocity structure functions for tracers and inertial particles. We will especially discuss large, neutrally buoyant and small, heavy particles. The experiments are conducted in the center of von Karmann mixing flows at high Reynolds numbers using direct Lagrangian particle tracking. We will show that single time, single particle statistics are not sensitive to particle inertial for both particles; however, we observed an inertial effect on the two-time, or the two-particle statistics. We will also show that the preferential concentration (increase of the radial distribution function) measured in the center of the apparatus is caused by a decrease of the average particle number density as a function of the distance from the center of the apparatus, which is the statistical stationary point of the flow field. The work has been conducted with Mathieu Gibert and Haitao Xu.
HRTW02 2nd October 2008
10:00 to 10:30
CR Doering Statistically stationary stirring of a scalar sustained by steady sources and sinks
Stirring generally enhances mixing, aiding molecular diffusivity by amplifying scalar gradients. Scalars sustained by steady sources and sinks, however, may best be mixed by flows with optimal transport properties. In this talk we describe differences between transient and steady state mixing and discuss implications for the concept of effective (eddy) diffusion.
HRTW02 2nd October 2008
10:30 to 11:00
GL Eyink Turbulent Lagrangian dynamics of vortex and magnetic-field line
We do not understand the laws of motion of vortex and magnetic-field lines in high-Reynolds-number turbulent flows. The current lore is self-contradictory. On the one hand, vortex/magnetic-field lines are often assumed to wander and elongate nearly as material lines in the limit of small viscosity/resistivity, and thus also to intensify, as a consequence of the Kelvin/Alfvén theorems. On the other hand, the topology of the lines is assumed to be continuously altered by viscous/resistive reconnection, implying breakdown of those same theorems. We discuss experimental and numerical evidence that these laws are both sometimes observed and sometimes violated in high-Reynolds-number turbulence. Unfortunately, we have no rational criterion to say when the Kelvin/Alfvén theorems or the Helmholtz laws of frozen-in'' motion should hold and when they should not. The problem has grown more perplexing with the theoretical discovery of "spontaneous stochasticity" for Lagrangian particle evolution in a Kolmogorov inertial range. As a consequence of the forgetting of initial separations in Richardson pair-diffusion, Lagrangian trajectories are not unique and must be replaced with random distributions of trajectories in the limit of small viscosity. This result presents a major crisis to our understanding of the turbulent dynamics of vortex/magnetic-field lines. As a possible resolution, we discuss a conjectured generalization of the Kelvin/Alfvén theorems, namely, that they survive as "backward martingales" of the spontaneous stochastic flows at high Reynolds-number. This conjectured relation provides a precise mathematical framework for the theory of turbulent reconnection. We discuss current rigorous results related to the conjecture and also important questions for investigation by experiment and simulation.
HRTW02 2nd October 2008
11:30 to 12:00
Intermittency and scaling of passive scalar convected by isotropic steady turbulence under the uniform mean scalar gradient
It has been more convincing that passive scalar in turbulence is more intermittent than the turbulent velocity field itself, implying that the small scales of the passive scalar are more affected by the large scale conditions. In order to get more precise knowledge about the scaling behavior of the passive scalar for various Reynolds (Peclet) numbers and large scale conditions, we have performed very high resolution direct numerical simulations (DNSs) of the passive scalar turbulence with or without uniform mean scalar gradient up to $2048^3$ grid points and $R_\lambda\approx 600$, and analysed the various statistical functions. Turbulent velocity field was statistically in a steady and isotropic state by Gaussian random force applied at large scales. Fundamental statistics such as the spectra of the kinentic energy, pressure, scalar variance, scalar-velocity flux were examined, especially in their scaling behavior. It is found that although curves of the kinetic energy and scalar spectra are well collapsed onto a single curve when the Kolmogorov variables are used, while the others are not as well as the former, suggesting need of more elaborated scaling. The scaling of the velocity structure functions is consistent with the existing data of experiments and DNSs, while the scaling of the passive scalar is not convincing and difficult to reach definite conclusion. When the isotropic random injection for the passive scalar is applied at large scales (Case R), each curve of the local scaling exponent at a given order has one local minimum and maximum point, unlike the velocity case, and plateau is not wide enough to precisely determine the scaling exponents. On the other hand, when the uniform mean scalar gradient is applied (Case G), the curves of the local scaling exponents of the isotropic sector are found to have well developed plateau, and their plateau levels are smaller than those of Case R, meaning stronger intermittency for the Case of G. Crossover of the velocity and scalar structure functions is also examined. The crossover of the transverse velocity structure functions is found to be very similar to that of the passive scalar. We seek the reason for the above differences and similarities.
HRTW02 2nd October 2008
12:00 to 12:30
PK Yeung Local flow structure and Reynolds number dependence of Lagrangian statistics in direct numerical simulations of homogeneous turbulence
Reynolds number dependence including the effects of intermittency is a crucial issue in the study of Lagrangian statistics and in how information from direct numerical simulations can be useful for stochastic modeling. Intermittency in the form of localized regions of intense straining or rotation is, for example, expected to influence how rapidly a fluid particle undergoes acceleration, and how multiple diffusing fluid particles move apart from each other. An effective approach to delineate such effects is to compute Lagrangian statistics conditioned on energy dissipation rate, enstrophy, or pseudo-dissipation following fluid particle trajectories. In this talk we shall illustrate these issues via recent results from simulations of isotropic turbulence at Reynolds numbers sufficiently high for observing inertial range behavior in the Eulerian (but not necessarily Lagrangian) frame. We also discuss research directions in the near future, including flows of greater complexity, and the promise of simulations at ever-increasing grid resolution that rapid advances in computing power are expected to make feasible.
HRTW02 2nd October 2008
14:00 to 14:30
Relative dispersion and Richardson’s constant
This talk will describe some very recent analysis of Direct Numerical Simulation results for turbulent relative dispersion over a wide range of Reynolds numbers. We will start with some background discussion of the nature and significance of relative dispersion and of the role of Kolmogorov’s similarity theory, leading to the introduction of Richardson’s constant as a fundamental parameter of relative dispersion. Although it is of great fundamental and practical significance, Richardson’s constant has not been well-quantified, and model estimates for it range from 0.01 to 4. We will describe first a traditional analysis of relative dispersion data, concluding that this approach does not yield a good estimate for Richardson’s constant even at the highest Reynolds number currently available. We then use a modified version of a new approach developed by Ott & Mann (JFM, 422, 207, (2000)) to show that a well-defined Richardson scaling range exists in our data. We estimate Richardson’s constant over a range of Reynolds numbers showing that it decreases weakly with Reynolds number to an asymptotic value at large Reynolds number of 0.55 - 0.57.
HRTW02 2nd October 2008
14:30 to 15:00
Dynamics of inertial particles in fully developed turbulence
We focus on acceleration of inertial particles, using experimatal measurements and numerical studies. In the experiment, particles are optically tracked in a turbulent ï¬‚ow of water using an Extended Laser Doppler Velocimetry technique. The probability density functions (PDF) of particle accelerations and their auto-correlation in time are computed. Numerical results are obtained from a direct numerical simulation in which a suspension of passive pointwise particles is tracked, with the same ï¬nite density and the same response time as in the experiment. We observe that many effects cannot be accounted for by point-particle models. We show that a much better description is achieved when one includes Faxen corrections in the particle's equation of evolution.
HRTW02 2nd October 2008
15:30 to 16:00
Mixing due to Rayleigh-Taylor instability
Rayleigh-Taylor instability occurs when a dense fluid rests on top of a light fluid in a gravitational field. It also occurs in an equivalent situation, in the absence gravity, where there is a pressure gradient normal to a interface between fluids of different density such that the direction of acceleration is from the light to the heavy fluid. This situation occurs in Inertial Confinement Fusion Implosions (ICF), see for exapmle Amemdt et al [1].

There have been a number of successful experiments on mixing due to Rayleigh-Taylor instability, for example Dimonte [2] and Dalziel [3]. However, it is impractical to perform the "perfect" experiment and experimental diagnostics are necessarily limited. High-resolution Large Eddy Simulation (LES) can now be used to greatly add to our understanding of the mixing processes and this is the subject of the talk. The numerical technique used,the TURMOIL code, was first used for Rayleigh-Taylor mixing by Youngs[4]. A MILES approach is used because of the need to treat discontinuities in the flow e.g. the initilal density discontinuity and shock waves (in some applications). The high Reynolds case is of most interest where it is assumed that the bulk properties of the turbulent zone are independent of the Reynolds number. It is argued that LES (rather that DNS) is then an appropriate technique. Mesh convergence, or near-mesh convergence, will be demonstrated for key statistical averages.

Results are discussed for a range of situations-(a) Rayleigh-Taylor mixing at a plane boundary, (b) three-layer Raleigh-Taylor mixing and (c) mixing in a spherical implosion (a simplified version of an ICF implosion).The three cases are illustrated in figs 1,2 and 3 in the attached file. Two main aspects of the mixing process will be discussed. Firstly the influence of initial conditions. It is argued that loss of memory of initial conditions is unlikely to occur in experimental situations. The initial conditions have a significant effect on the overall width of the mixing zone - an important issue for engineering models. It would very difficult to obtain corresponding results experimentally because of the lack of control and the difficulty in measuring initial conditions. Secondly, the internal structure of the turbulent mixing zone will also be discussed, in particular the dissipation of both turbulence kinetic energy and of density fluctuations. For the internal structure results are more universal and less dependent on the initial conditions.

1. P. Amendt et al., “Indirect-drive noncryogenic double-shell ignition targets for the National Ignition Facility: Design and analysis”, Physics of Plasmas, 9, p2221, (2002). 2. G Dimonte & M Schneider, “Density ratio dependence of Rayleigh-Taylor mixing for sustained and impulsive acceleration histories”, Physics of Fluids, 12, p304 (2000) 3. S.B.Dalziel, "Self-similarity and internal structure of turbulence induced by Rayleigh-Taylor instability", J. Fluid Mech. 399, p1,

HRTW02 2nd October 2008
16:00 to 16:30
K Schneider Lagrangian acceleration in confined 2d turbulent flow
A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer, is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20. Related Links * http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.3139v1.pdf - PDF file of a preprint to appear in PRL
HRTW02 2nd October 2008
16:30 to 17:00
CM Casciola Clustering of inertial particles in shear flows
Recently, clustering of inertial particles in turbulence has been thoroughly analyzed for statistically homogeneous and isotropic flows. The most striking result concerns the singular behavior exhibited by the radial distribution function under proper resonance conditions, showing clustering below the Kolmogorov scale. Since anisotropy is strongly depleted through the inertial range, the advecting field anisotropy may be expected in-influential for the small scale features of particle configurations. By addressing direct numerical simulations (DNS) of a statistically steady particle-laden homogeneous shear flow, we find instead that the small scales of the particle distribution are strongly affected by the geometry of velocity fluctuations at large scales. The proper statistical tool is the angular distribution function of particle pairs (ADF). Its anisotropic component may develop a singularity whose strength quantifies the anisotropy of the small scale clustering. The data provide evidence that the process is essentially anisotropic, even in the range of scales where isotropization of velocity statistics already occurred. Possible implications and connections of the above findings for turbophoresis in wall bounded shear flows will be briefly outlined using DNS data of particle laden turbulent pipe flows as example.
HRTW02 2nd October 2008
17:10 to 17:40
D Thomson The behaviour of particle pairs in kinematic simulations
The way pairs of particles separate is an important aspect of turbulent mixing which has often been explored using the technique of kinematic simulation. However kinematic simulation is not like real turbulnce in that the Fourier modes are independent and the smaller eddies are not advected (or 'swept') by the large eddies. Our aim here is to explore this aspect of kinematic simulation both theoretically and numerically. The fact that the small eddies are not swept by the large eddies, but the particles in the flow are so swept, means that particle pairs are swept through the smaller eddies by the large eddies. This is expected to alter the time scale on which the relative velocity of the particles fluctuates. A simple argument then shows that the mean square separation of pairs is expected to grow, not as t cubed as expected following Richardson, but as t to the sixth power. This is confirmed in numerical simulations where we add a mean flow to the kinematic flow field to exaggerate the problem caused by lack of sweeping (with the eddies not being advected by the mean flow). Without the mean flow the situation is more complex with a significant contribution to the separation process from locations where the velocity is small and where there is no sweeping issue. This leads to a separation growing like t to the power 9/2. The time dependence of the kinematic flow field can also lead to a wider range of behaviours. The work described here is not especially new (we published the main idea in 2005) but it remains controversial and we hope the talk will generate some discussion of the ideas involved.
HRTW02 2nd October 2008
17:40 to 18:10
R Rubinstein Closure theories for inhomogeneous turbulence
Although Kraichnan formulated the Direct Interaction Approximation and the Test-Field model for general problems of inhomogeneous turbulence, the resulting equations, requiring repeated multiple integrations over the flow domain, are both difficult to understand and difficult to apply in practice; in the homogeneous case, triad interactions provide the key to unraveling the physics of the approximation. The goal of this work is to formulate the closure theory of some special inhomogeneous problems with comparable simplicity. It is done by decomposing the inhomogeneous problem into a set of coupled quasi-homogeneous problems, each of which admits a simple formulation. The formalism will be applied to the problem of weakly inhomogeneous turbulence, where previous heuristic theories have been incomplete. The same formalism applies to problems admitting scaling transformations; it will be applied to give a simple formulation of the problem of turbulence in a half-space.
HRTW02 3rd October 2008
09:40 to 10:10
Stratified turbulence: a possible interpretation of some geophysical turbulence measurements
Several existing sets of smaller-scale ocean and atmospheric data appear to display Kolmogorov-Obukov-Corrsin inertial ranges in horizontal spectra for length scales up to at least a few hundred meters. It is argued here that these data are inconsistent with the assumptions for these inertial range theories. Instead, it is hypothesized that the dynamics of stratified turbulence explain these data. If valid, these dynamics may also explain the behavior of strongly stratified flows in similar dynamic ranges of other geophysical flows.
HRTW02 3rd October 2008
10:10 to 10:40
Vertical dispersion by stratified turbulence
An analytical relation is derived for the growth of the vertical mean square displacement of fluid particles in stratified turbulence. A number of numerical simulations are carried out to test the analytical relation. The comparison shows good agreement between the analytical and the numerical results.
HRTW02 3rd October 2008
10:40 to 11:00
Divergent-rotational modes and passive scalars in stratified turbulence
Strongly stratified turbulent flows are anisotropic but have three-dimensional dynamics with a forward energy cascade as shown by Lindborg (2006). Simulations with hyperviscosity also revealed an inertial range with a horizontal k^-5/3-spectrum. We have continued this work and examined the features of divergent and rotational modes, and of passive scalars in the inertial range of stratified turbulence.

The Helmholtz decomposition of the velocity into a rotational and divergent part have been used to study vortices and internal waves in stratified flows. In flows with mainly vertically oriented vortices the rotational part dominates while the divergent part dominates when there are mainly internal waves. The timescale ratio of the 'fast' waves and the 'slow' horizontal vortical motions can be estimated as the vertical Froude number F_v = u/Nl_v, where u is a horizontal velocity scale, l_v a verti cal length scale, N the Brunt-Vaisala frequency. It is often assumed that F_v = 0 in strongly stratified flows suggesting separate time scales of vortices and waves, and consequently weak interactions. However, scaling analysis suggests l_v = u/N in stratified turbulence, i.e. F_v = 1, which was supported by DNS (Brethouwer et al. 2007). In stratified turbulence the divergent and rotational modes may thus have similar timescales leading to strong nonlinear interactions between rotational and dive rgent modes. This implies that forcing in either divergent or rotational modes may have minor effects on the inertial range dynamics of stratified turbulence. Results of simulations with different stratification and resolution show that the energy of divergent and rotational modes hav e the same magnitude in the inertial range when large-scale rotational modes are forced, see Lindborg & Brethouwer (2007). In the simulations with forcing of divergent modes, small horizontal wave numbers and one vertical wave number are forced which introduces a vertical length scale. Results show that the inertial range spectra are very similar in simulations with forcing of rotational modes and divergent modes, suggesting similar dynamics, if in the latter simulations the large-scale dynamics o beys F_v = 1, but deviations are found when this condition is not fulfilled. The next subject is a passive scalar in stratified turbulence. The Obukhov-Corrsin theory for the one-dimensional spectrum of the variance of a passive scalar in the Kolmogorov inertial range of turbulence predicts a k^-5/3 slope. The second-order structure function according to the same theory has a r^2/3 power-law range. Measurements of horizontal spectra and structure functions of passive scalars (e.g. ozone) in the mesoscale range of the middle atmosphere are consistent with this theory. This is remarkable because the mesoscale range is strongly stratified and does not resemble Kolmogorov turbulence. We have carried out numerical simulations of stratified turbulence with large-scale forcing, hyperviscosity

HRTW02 3rd October 2008
11:30 to 12:00
Transition in energy spectrum for forced stratified turbulence
Energy spectrum for forced stably stratified turbulence is investigated numerically by solving the 3D Navier-Stokes equations under the Boussinesq approximation with stochastic forcing applied to the largest velocity scales. Using pseudo-spectral simulations with 1024^3 grid points, we could verify the transition in the vortex (horizontal) spectrum (as a function of horizontal wave number) from $k_{\perp}^{-3}$ to $k_{\perp}^{-5/3}$. Meanwhile the wave spectra shows $k_{\perp}^{-2}$ for the large scales, and $k_{\perp}^{-5/3}$ for the small scales. According to Carnevale {\it et.~al.}, the transition wave number is understood as the Ozmidov scale with a correction by the coefficients of the buoyancy spectrum, $E(k) =\alpha N^2k^{-3}$, and the Kolmogorov spectrum, $E(k)=C_K\epsilon^{2/3} k^{-5/3}$. By equating these spectra, $k_b \sim (\alpha/C_K)^{3/4}\sqrt {N^3/ \epsilon}$ is obtained for the transition wavenumber. Our calculation shows, however, that the vortex spectra at large scales seem to have the same slope irrespective of stratification, which implies a possibility of a different mechanism for producing the $k_{\perp}^{-3}$ spectrum. We will discuss possibility that the spectrum corresponds to two-dimensional turbulence. Referece: Carnevale,G.F. {\it et.~al}: 2001 J.~Fluid Mech. {\bf 427} 205--239.
HRTW02 3rd October 2008
12:00 to 12:30
Non-Oberbeck-Boussinesq effects in Rayleigh-Benard convection
The problem of Rayleigh-Benard convection is commonly analyzed within the so-called Oberbeck-Boussinesq (OB) approximation, in which the fluid properties are assumed to be temperature independent, apart from the density for which a linear temperature dependence is assumed. Under normal conditions, i.e., small temperature differences between the bottom and top plate, this approximation is rather good. However, in order to achieve ever larger Rayleigh numbers for given cell height and fluid properties the temperature difference is quite frequently increased to such an extent that the OB approximation has to be expected to fail. Non-Oberbeck-Boussinesq (NOB) effects on the mean center cell temperature, the Nusselt number Nu, and the Reynolds number Re then have to be expected at the largest Rayleigh numbers. We report on our recent experimental, theoretical, and numerical results on these NOB corrections. For water and glycerol they are governed by the temperature dependences of the kinematic viscosity and the thermal diffusion coefficient: With increasing NOBness, for water and glycerol Nu goes down and the center temperature goes up, whereas for ethane gas in general Nu goes up and the center temperature goes down. However, for ethane close to the critical point the main origin of NOB corrections lies in the strong temperature dependence of the isobaric thermal expansion coefficient, namely in the nonlinear temperature dependence of the density, leading to NOB corrections which presently cannot be described by our extended Prandtl-Blasius boundary layer theory. Related Links * http://pof.tnw.utwente.nl/ - Web page Phyiscs of Fluids group Twente
HRTW02 3rd October 2008
14:00 to 14:30
Y Zhou Scaling criteria for high Reynolds and Peclet number turbulent flow, scalar transport, mixing, and heat transfer
Very high Reynolds (Re) and Peclet (Pe) number turbulent flows are commonly encountered in engineering, geophysical and astrophysical applications. In comprehensive statistical flow experiments or corresponding direct numerical simulations of high Re and Pe number turbulent flow, scalar transport, mixing, and heat transfer the energetic excitation influences of the entire range of dynamic spatial scales combining both velocity fluctuations and passive scalar variances must be considered together. However, direct computational simulations or experiments directed to the very high Re and Pe flows of practical interest commonly exceed the resolution possible using current or even foreseeable future super computer capability or spatial, temporal and diagnostic technique limitations of current laboratory facilities. Pragmatic considerations and practical needs promote use of statistical flow data bases developed from direct numerical simulations or experiments at the highest Re and Pe levels achievable within the currently available facility limitations. Unfortunately the obtainable levels are lower than those associated with the flows of practical interest. Moreover, at present, there is no metric to indicate whether and how much of the fully resolved physics of the flow of interest has been captured within the facilities available to the investigator. This talk presents metric criteria based on establishing a smaller subset of the total range of dynamic scale interactions that will still faithfully reproduce all of the essential, theoretically significant, influences of the complete range of scale interactions associated with the flows of practical interest. The present work leads to the identification of the minimum significant Re flow and Pe field that a researcher must attain in direct simulation or experiment (hereafter called the minimum state). These threshold criteria levels are minimum values to be attained in experiments or direct simulations which assure that the energy-containing scales of the flows ? and scalar fields under investigation are not contaminated by the (non-universal) velocity dissipation and scalar diffusivity inertial range scale limits.
HRTW02 3rd October 2008
14:30 to 15:00
Numerical study of 3D Rayleigh-Taylor turbulence
The Rayleigh-Taylor turbulence in 3D space is numerically studied via the Boussinesq approximation along the same line as the 2D numerical study by Celani et al. (2006 Phys.Rev.Lett. 96 134504). A comparison with the phenomenology proposed by Chertkov (2003 Phys.Rev.Lett. 91 115001), in particular deviation from the phenomenology (intermittency), will be presented.
HRTW02 3rd October 2008
15:30 to 16:00
Some remarks on the dissipative properties of homogenous and isotropic turbulence
Dissipation of kinetic energy plays a key role in understanding the statistical properties of turbulence. In this talk, we shall review some recent results obtained by performing high resolution numerical simulations of homogenous and isotropic turbulence. In particular, we present an exhaustive investigation of the statistics of velocity gradients along the trajectories of neutral tracers and of heavy/light particles advected by an homogeneous and isotropic turbulent flow. We propose a Lagrangian rephrasing of the Refined Kolmogorov Similarity Hypothesis (RKSH) and test its validity along the particle trajectories. We also show that for homogenous and isotropic compressible turbulence, there is no statistical differences in the statistical properties of inertial range intermittency due either to the slight compressibility or to the different dissipative mechanism.
HRTW02 3rd October 2008
16:00 to 16:30
CF Barenghi Reconnection of superfluid vortex bundles
Using the vortex filament model and the Gross Pitaevskii nonlinear Schroedinger equation, we show that bundles of quantised vortex lines in helium~II are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence and show that, during the bundle reconnection process, a large amount of Kelvin waves is generated, in agreement with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows.
HRT 6th October 2008
15:00 to 16:00
D Dritschel Inviscid two-dimensional turbulence
HRT 7th October 2008
13:00 to 14:00
Pressure-driven turbulent puff in a pipe
HRT 8th October 2008
14:00 to 15:00
D Dritschel Inviscid two-dimensional turbulence: the sequel
HRT 8th October 2008
15:00 to 16:00
Helical flows, conservation laws and symmetries
HRT 9th October 2008
15:00 to 16:00
Stratified turbulence in the atmosphere and the oceans
HRT 14th October 2008
15:00 to 16:00
Scalar transport
HRT 21st October 2008
15:00 to 16:00
Possible intertial range dynamics in strongly stratified flows
HRT 23rd October 2008
15:15 to 16:15
Conservation principles, statistical invariants, and energy decay laws in homoegeneous turbulence
HRTW02 26th October 2008
17:40 to 18:10
Scale-invariance in three-dimensional isotropic turbulence
We present a critical review of the Kolmogorov (1941) theory of isotropic turbulence, with particular reference to the 2/3' power-law for the second-order structure function (and the corresponding -5/3' law for the energy spectrum). We begin by noting that the recent resolution of an associated paradox allows the inertial range to be defined in terms of the scale-invariance of the energy flux (David McComb, J. Phys. A: Math. Theor. 41, 075501 (2008)), thus permitting the Kolmogorov arguments to be presented independently of concepts such as localness which are themselves counter-intuitive when interpreted in terms of vortex-stretching. If this approach is pursued further, then a simple phenomenological analysis shows that we can regard turbulence as a statistical field theory possessing one nontrivial fixed point (corresponding to the top of the inertial range) and two trivial fixed points at the origin and infinity, respectively, in wavenumber space. Using this framework, various schools of criticism, ranging from the original criticism by Landau (1959), through intermittency corrections' to present-day analogies with the theory of critical phenomena, with the introduction of anomalous exponents', are analysed. In particular, we examine the conflict between the recent work of Lundgren (2002), which uses mathematical arguments to show that the 2/3' law must be asymptotically true in the limit of infinite Reynolds numbers; and that of Falcovich which uses mathematical arguments to show that the 2/3' law is incompatible with the observed values for higher-order moments. We conclude by attempting to put forward a picture in which various long-standing contentious issues may be seen as either resolved or at least potentially resolvable.
HRT 27th October 2008
14:00 to 15:00
Wave breaking
HRT 27th October 2008
15:30 to 16:30
Absolute zero: a history of 400 years of thermodynamics
HRT 29th October 2008
15:00 to 16:00
Vortex rings
HRT 29th October 2008
16:30 to 17:30
Absolute zero: a history of 400 years of thermodynamics
HRT 30th October 2008
14:30 to 15:30
A round table discussion on turbulent cascades and vortex dynamics
HRTW06 31st October 2008
09:45 to 10:00
Remarks on the Aussois 2007 meeting
HRTW06 31st October 2008
10:00 to 11:00
Scaling implied by circulation collapse
HRTW06 31st October 2008
11:00 to 12:00
Inviscid colliding Lamb dipoles
HRTW06 31st October 2008
12:30 to 13:30
Weak Solutions of Hydrodynamic Equations
HRTW06 31st October 2008
13:30 to 14:30
K Ohkitani Pressure Hessian and dynamics of the Jacobian matrix
HRTW06 31st October 2008
14:40 to 15:40
Cascades, thermalisation and eddy viscosity in helical Galerkin truncated Euler flows
HRTW06 31st October 2008
17:00 to 18:00
Spectral energy transfer
HRTW03 3rd November 2008
13:15 to 14:00
F Sahroui Phase coherence, structures, intermittency in magnetised space plasmas
HRTW03 3rd November 2008
14:00 to 14:45
D Dritschel Inviscid shallow water turbulence
HRTW03 3rd November 2008
15:15 to 16:00
Momentum transport in fusion devices due to small scale turbulence
HRTW03 3rd November 2008
16:45 to 17:00
Coherent structures in accretion-disk turbulence
HRTW03 3rd November 2008
17:00 to 17:15
M Bustamante New results on nonlinear resource dynamics
HRTW03 4th November 2008
09:00 to 09:40
M McIntyre There's no such thing as turbulence without waves: reflections on Jupiter and the several different Rhines scales
HRTW03 4th November 2008
09:40 to 10:20
Numerical study of a two-dimensional internal gravity wave attractor
HRTW03 4th November 2008
10:50 to 11:30
P Bartello Wave saturation in stratified turbulence
HRTW03 4th November 2008
11:30 to 12:10
A mechanism for reversals of large scale fields driven by turbulence
HRTW03 4th November 2008
13:40 to 14:20
Nonlinear evolution of the zigzag instability in stratified fluids: a shortcut on the route to dissipation
HRTW03 4th November 2008
14:20 to 15:00
Flows in a precessing sphere
HRTW03 4th November 2008
15:30 to 16:10
The QNSE theory of ansiotropic turbulence and waves in flows with stable stratification
HRTW03 4th November 2008
16:10 to 16:50
Structure formation in rotating, stratified and MHD turbulence
HRTW03 4th November 2008
16:50 to 17:30
The stochastic Orr mechanism and the fluctuations of self-organised 2D turbulent flows
HRTW03 4th November 2008
17:30 to 18:10
Spherical shallow water turbulence: cyclone-anticyclone asymmetry, potential vorticity homogenisation and jet formation
HRTW03 5th November 2008
09:00 to 09:40
S Cowley Anisotropic structure in fusion turbulence
HRTW03 5th November 2008
09:40 to 10:20
S Galtier Structures and waves in anisotropic MHD turbulence
HRTW03 5th November 2008
10:50 to 11:30
The excitation of inertial-acoustic waves in turbulent accretion disks
HRTW03 5th November 2008
11:30 to 12:10
Nonlinear dynamos in accretion disc turbulence
HRTW03 5th November 2008
13:40 to 14:20
E Lee Paradigmatic flows for small-scale magnetohydrodynamics based on symmetric design: properties of ideal and dissipative simulations
HRTW03 5th November 2008
14:20 to 15:00
Predictability of rotating stratified turbulence
HRTW03 5th November 2008
15:30 to 16:10
Modulational instability of Rossby/drift waves and generation of zonal jets
HRTW03 5th November 2008
16:10 to 16:50
O Alexandrova Anisotropy and dissipation in space plasma turbulence
HRTW03 5th November 2008
16:50 to 17:30
A Schekochihin Weak Alfen-wave turbulence revisited
HRTW03 6th November 2008
09:00 to 09:40
Nonlinear waves and coherent vortices in beta-plane turbulence
HRTW03 6th November 2008
09:40 to 10:20
Scalar transport and diffusion in smooth flows
HRTW03 6th November 2008
10:50 to 11:30
Formation of multiple zonal jets in the ocean
HRTW03 6th November 2008
11:30 to 12:10
Frontal instabilities in a differentially rotating stratified fluid
HRTW03 6th November 2008
13:40 to 14:20
A Thompson Scaling baroclinic eddy fluxes: vortices and jets
HRTW03 6th November 2008
14:20 to 15:00
Scale-by-scale budgets, anisotropy and inhomogeneity in soft convective turbulence
HRTW03 6th November 2008
15:30 to 16:10
Free-wave trapped-wave resonances in oceanic waveguides
HRTW03 6th November 2008
16:10 to 16:50
Very inhomogeneous/anisotropic turbulence near interfaces - the key to most turbulence structures
HRTW03 6th November 2008
16:50 to 17:30
Cascades and structure functions in the atmospheric boundary layer
HRTW03 6th November 2008
17:30 to 18:10
Structure functions, intermittency and dimensionality of decaying rotating turbulence
HRTW03 7th November 2008
09:00 to 09:40
Waves and eddies in rotating flows at moderate Rossby and large Reynolds numbers and the possibility of new scaling laws in the presence of helicity
HRTW03 7th November 2008
09:40 to 10:20
Zonal flows in two-dimensional MHD turbulence
HRTW03 7th November 2008
10:50 to 11:30
Rotating and/or MHD turbulence with imposed magnetic field: recent progresses using axisymmetric (strongly anisotropic) statistical triadic closure
HRTW03 7th November 2008
13:40 to 14:20
T Yousef Alfen wave turbulence - some new numerical results
HRTW03 7th November 2008
16:00 to 17:00
K Moffatt Magnetostrophic turbulence driven by buoyancy
HRT 10th November 2008
15:00 to 16:00
Waves and turbulence
HRT 11th November 2008
15:00 to 16:00
Turbulent vortex rings
HRT 12th November 2008
15:00 to 16:00
Smashing vortices
HRT 14th November 2008
15:00 to 16:00
P Bartello Two-timescale analysis of stratified turbulence, potential vorticity, and statistical mechanics
OFB001 17th November 2008
16:05 to 16:50
Turbulence in fluids, its pervasive nature, control and use
HRT 18th November 2008
15:00 to 16:00
An introduction to turbulence: a tutorial for the non-specialist
HRT 19th November 2008
15:00 to 16:00
R Kerswell Producing bounds on turbulence
HRT 25th November 2008
15:00 to 16:00
Bifurcations in the flow along pipes and channels
HRT 27th November 2008
15:00 to 16:00
A simple model for solar iso-rotation contours
HRT 28th November 2008
15:00 to 16:00
Structure and spectra in MHD dynamos
HRT 2nd December 2008
15:00 to 16:00
A mechanism for magnetic field reversals
HRT 5th December 2008
15:00 to 16:00
Why study isotropic turbulence?
HRTW04 8th December 2008
09:20 to 09:30
Introduction
HRTW04 8th December 2008
09:30 to 10:00
P Rhines Eddies and circulation: lessons from oceans, atmospheres and the GFD lab
Planetary fluids inherit the angular momentum of their planets. Concentrated and diluted, and fragmented into potential vorticity (PV), angular momentum controls the circulation under a limited budget of energy. In particular, wherever energy decays, planetary PV takes control of the dynamics. This so-called β-control is manifested in the ‘stiffness’ and scale-dependent ‘PV elasticity’ of rotating fluids which leads to many kinds of wave motion, and to limitation of turbulent mixing. The fluid finds ways, for example PV staircases and their attendant jets, of dealing with limited energy and PV control. Momentum rearrangement that follows stirring of the PV field by eddies is a key process. We see numerous zonal jets on the rapidly rotating, gas giants (strong β-control), and a weaker β-control over Earth’s subpolar atmospheric jet streams, where the kinetic energy density averages 10^6 J m^-2. The Earth’s oceans, operating at lower kinetic energy levels (10^4 J m^-2). have selected jets of much finer scale, and a dominant energy-containing eddy mode manifested as dimples on the sea surface, simply marching westward. These are strongly nonlinear baroclinic Rossby waves which do not obey the simple rules of geostrophic turbulence, namely, expansion of scale laterally and vertically toward a barotropic state, and coalescence into sparsely distributed hard-core vortices. A second mode of oceanic eddy that is widespread is the (equivalent-) barotropic mode of geostrophic flow, ‘tall’ eddies which are highly coordinated with bottom topography. Here we describe field observations and simulations from the GFD laboratory. These demonstrate Rossby wave propagation, induction of zonal circulation and inhibition of mixing which leads to the ‘ozone hole’ in the terrestrial southern stratosphere; also transition between Rossby waves and solitary eddies which transport fluid (as in the world’s oceans), topographic production of eddies and waves, with steering by PV waveguides (formed by topography and circulation). Using a new laboratory technique known as ‘optical altimetry’ we now can see the interaction of unbalanced flows (downslope winds, gravity- and inertial waves) with the energy-containing geostrophic eddies, as seen in the upward radiation of gravity waves as storms encounter the Greenland’s icy topography.
HRTW04 8th December 2008
10:00 to 10:30
Jet formation and transport in baroclinic turbulence with simple topography
Jets are a well-known feature of the Southern Ocean's Antarctic Circumpolar Current. Evidence from satellite altimetry and numerical models suggests that zonal jets are also a robust feature of the mid-latitude ocean basins. The characteristics of mid-latitude and Southern Ocean jets differ significantly, with the latter having narrow, ribbon-like appearances and a greater tendency to merge, migrate and meander. Topography, lack of meridional boundaries, and variations in the strength and vertical structure of mean flows all contribute to the dissimilarity of mid-latitude and Southern Ocean jets. This study considers the influence of simple topography--sinusoidal ridges and bumps--on the formation and transport properties of coherent structures (jets and eddies) in forced-dissipative, quasi-geostrophic turbulence. The experimental framework is a series of two-layer, baroclinically-unstable simulations in a doubly-periodic domain. Transport and mixing properties are diagnosed using the Nakamura effective diffusivity. In simulations with zonal ridges, the upper layer, in particular, feels a competition between the imposed topographical scale (ridge separation) and the Rhines scale. This can lead to unsteady jet structure and vertical misalignment of transport barriers. Three-dimensional topography with a sufficiently large amplitude may induce periodic bursts of high eddy kinetic energy related to baroclinic instability acting on topographically steered non-zonal mean flows. These episodes allow large-scale reorganization of the jet structure. It is likely that these features play a key role in the dynamic nature of Southern Ocean jets.
HRTW04 8th December 2008
10:30 to 11:00
The turbulent equilibration of an unstable baroclinic jet
The evolution of an unstable baroclinic jet, subject to a small perturbation, is examined numerically in a quasi-geostrophic two-layer channel model. After a period of initial wave growth, wave breaking leads to two-dimensional turbulence within each layer, and to the eventual equilibration of the flow. The equilibrated flow must satisfy certain constraints; its total momentum is conserved, its total energy is bounded and the flow must be realizable via some area preserving (diffusive) rearrangement of the potential vorticity field of the initial flow. A theory is introduced that predicts the equilibrated flow in terms of the initial flow parameters. The idea is that the final state minimizes available potential energy, subject to constraints on the total momentum and total energy, and the further constraint that the potential vorticity changes through a process of complete homogenization within well-delineated regions in each layer. Within a large region of parameter space, the theory is found to accurately predict the cross-channel structure and strength of the equilibrated jet, the regions where potential vorticity mixing takes place, and total eddy mass (temperature) fluxes.
HRTW04 8th December 2008
11:30 to 12:00
Inertial instability in rotating and stratified flow
The unfolding of inertial instability in vortices in a uniformly rotating and stratified fluid is studied through numerical simulations. The vortex dynamics during the instability is examined in detail. We demonstrate that the instability is stabilized via redistribution of angular momentum in a way that produces a new equilibrated vortex with a stable velocity profile. Based on extrapolations from the results of a series of simulations in which the Reynolds number and strength of stratification are varied, we arrive at a construction based on angular momentum mixing that predicts the infinite-Reynolds-number form of the equilibrated vortex toward which inertial instability acting alone would drive an unstable vortex. The essential constraint is conservation of total absolute angular momentum. The construction can be used to predict the total energy loss during the equilibration process.
HRTW04 8th December 2008
12:00 to 12:30
Zigzag instability of vortex arrays in stratified and rotating fluids
We investigate the three-dimensional stability of columnar vertical vortex arrays (Karman street, double symmetric row of vortices) in a stratified and rotating fluid by means of an asymptotic theory for long-vertical wavelength and well-separated vortices. It is found that both the Karman street and the double symmetric row are unstable to the zigzag instability when the fluid is stratified independently of the background rotation. The zigzag instability bends the vortices with almost no internal deformation and ultimately slices the flow into horizontal layers. The results are in excellent agreement with direct numerical stability analyses. They may explain the formation of layers commonly observed in stratified flows.
HRTW04 8th December 2008
14:00 to 14:30
Instabilities of a columnar vortex in a stratified fluid
The stability of a columnar vortex in a stratified fluid is addressed theoretically and experimentally. In a first part, we show that the addition of a small tilt angle between the vortex axis and the density gradient direction changes drastically the structure and stability of the vortex. For Froude numbers larger than one, a strong axial flow is created around the critical radius where the angular velocity equals the Brunt-Vaisala frequency. For large Reynolds numbers, this axial flow is sufficiently localized in the critical layer to become unstable with respect to the shear instability. Theoretical predictions for the structure of the critical layer and the instability characteristics are compared with experimental results. In a second part, we analyse the stability of a vortex aligned along with the density gradient direction. We show that the linear modes of the vortex are weakly unstable for small Froude numbers. These modes are radiative at large radii, which means that the vortex generates internal waves spontaneously. At moderate Froude numbers, these radiative modes cease to be unstable. However, a resonance between the radiative modes and the Kelvin modes of the vortex becomes possible leading to instability in narrow wavenumber bands.
HRTW04 8th December 2008
14:30 to 15:00
Structure formation in rotating turbulence
We consider decaying rotating turbulence at a Rosby number of around unity. We show that the large-scale columnar structures so evident in many experiments and some simulations are created by linear wave propagation and not the result of triad interactions. We also discuss the reasons for the predominance of cyclones, and the mechanisms by which anisotopy feeds down to the small scales.
HRTW04 8th December 2008
16:00 to 16:30
Local transfer and spectra of a diffusive field advected by large-scale incompressible flows
This study revisits the problem of advective transfer and spectra of a diffusive scalar field in large-scale incompressible flows in the presence of a (large-scale) source. By large scale'' it is meant that the spectral support of the flows is confined to the wave-number region $k<k_d$, where $k_d$ is relatively small compared with the diffusion wave number $k_\kappa$. Such flows mediate couplings between neighbouring wave numbers within $k_d$ of each other only. It is found that the spectral rate of transport (flux) of scalar variance across a high wave number $k>k_d$ is bounded from above by $Uk_dk\Theta(k,t)$, where $U$ denotes the maximum fluid velocity and $\Theta(k,t)$ is the spectrum of the scalar variance, defined as its average over the shell $(k-k_d,k+k_d)$. For a given flux, say $\vartheta>0$, across $k>k_d$, this bound requires $$\Theta(k,t)\ge \frac{\vartheta}{Uk_d}k^{-1}.$$ This is consistent with recent numerical studies and with Batchelor's theory that predicts a $k^{-1}$ spectrum (with a slightly different proportionality constant) for the viscous-convective range, which could be identified with $(k_d,k_\kappa)$. Thus, Batchelor's formula for the variance spectrum is recovered by the present method in the form of a critical lower bound. The present result applies to a broad range of large-scale advection problems in space dimensions $\ge2$, including some filter models of turbulence, for which the turbulent velocity field is advected by a smoothed version of itself. For this case, $\Theta(k,t)$ and $\vartheta$ are the kinetic energy spectrum and flux, respectively.
HRTW04 8th December 2008
16:30 to 17:00
Singular focusing of sub-inertial internal waves on the non-traditional’ beta-plane
On the non-traditional' beta-plane internal waves propagating poleward partly penetrate through the inertial latitude and turn into sub-inertial waves which propagate further poleward trapped in the narrowing waveguides around the local minima of the buoyancy frequency. The present work addresses basic open questions about wave evolution and, in particular, its possible role in deep ocean mixing.
HRTW04 9th December 2008
09:30 to 10:00
Turbulent fluid dynamics at the margins of rotational and stratified control
Geophysical fluid dynamicists have developed a mature perspective on the dynamical influence of Earth's rotation, while most other areas of fluid dynamics can safely disregard rotation. Similarly, geophysical problems usually arise under the influence of stable density stratification at least as importantly as velocity shear. In this talk the dominant turbulence and wave behaviors in the rotating and non-rotating, stratified and non-stratified fluid-dynamical realms are described, and particular attention is given to their borderlands, where rotational and stratified influences are significant but not dominant. Contrary to the inverse energy cascade of geostrophic turbulence toward larger scales, a forward energy cascade develops within the borderlands from the breakdown of diagnostic force balances, frontogenesis, and frontal instabilities, and then it continues further through the small-scale, non-rotating, unstratified (a.k.a. universal) realm until it dissipates at the microscale. In particular, this submesoscale cascade behavior is of interest as a global route to kinetic and available-potential energy dissipations in the oceanic general circulation, as well as an energy source for microscale material mixing across stably-stratified density surfaces.
HRTW04 9th December 2008
10:00 to 10:30
P Bartello Quasigeostrophic and stratified boussinesq turbulence
Turbulence generated by random isotropic i.c.'s in the strongly stratified and rapidly rotating environment that characterises large-scale atmosphere/ocean flows, leads to nonlinear geostrophic adjustment via a downscale cascade of wave energy and a first-order decoupling of geostrophic modes from linear wave modes. The march toward ever higher resolution in "realistic" models has renewed the community's interest in smaller-scale stratified turbulence with weak rotation, where this large-scale decoupling is reduced. Proceeding to even smaller scales, i.e. L~H~U/N, where L and H are the horizontal and vertical length scales and N is the Brunt-Vaissalla frequency, 3-d overturning may occur (Thorpe 1977). Our recent non-rotating simulations of stratified flow show that, if the Reynolds number is sufficiently high, then the characteristic vertical scale decreases until the usual Froude number (U/NH) reaches order unity from below, where it saturates. Increasing the stratification decreases the Froude number based on the horizontal scale. Rescaling the equations in this way yields hydrostatic flow where the vertical advection term is not small. On the other hand, if the vertical scale of the flow is set by viscosity, weak rotation or, for some period of time, by the initial conditions, the classical quasi-horizontal layered flow of Riley, Metcalfe & Weissman (1981) is recovered. We also simulated how this picture changes with the addition of varying rotation rates in order to observe the transition from stratified to quasigeostrophic (QG) turbulence. Throughout this work we examined the statistics of linear wave and vortical (PV) modes separately. It was shown that, although they form a complete basis, they can only be expected to have dynamical relevence when U/NH
HRTW04 9th December 2008
10:30 to 11:00
Effects of large-scale energy dissipation in geostrophic turbulence
We compare the distinct effects of frictional damping and radiative, or thermal, damping on the equilibration of two-dimensional geostrophic turbulence. The spatial distribution of energy in both physical and spectral space is examined with particular attention to the distribution of coherent vortices, which are found to be ubiquitous with either form of large-scale energy dissipation. Consideration of the stochastically forced vorticity equation suggests that in the case of frictional damping, maximum vorticity values depend on the damping coefficient $r$ through \qext$\sim r^{-1/2}$, while in the case of thermal damping \qext is approximately independent of damping coefficient. These are well-supported by numerical experiments. The difference between frictional and thermal damping becomes striking in simulations of forced shallow water turbulence on the sphere. While shallow-water models have been successful in reproducing the formation of robust, and fully turbulent, latitudinal jets similar to those observed on the giant planets, they have to date consistently failed to reproduce prograde (superrotating) equatorial winds. Here it is demonstrated that shallow water models not only can give rise to superrotating winds, but do so very robustly, provided that the physical process of large-scale energy dissipation by radiative relaxation (thermal damping) is taken into account. With appropriate choice of thermal damping rate, equatorial superrotation can be achieved at apparently any deformation radius.
HRTW04 9th December 2008
11:30 to 12:00
Two-dimensional turbulence inside a strong vortex
I will present experimental results on turbulence generated in thin fluid layers in the presence of a large-scale coherent flow, or a spectral condensate. It will be shown that the condensate modifies the third-order velocity moment in a much wider interval of scales than the second one. The modification may include the change of sign of the third moment in the inverse cascade. This observation may help resolve a controversy on the energy flux in meso-scale atmospheric turbulence (10-500 km): to recover a correct energy flux from the third velocity moment one needs first to subtract the coherent flow. We find that the condensate also increases the velocity flatness. I will briefly present a theoretical consideration for condensate-turbulence interaction.
HRTW04 9th December 2008
12:00 to 12:30
N Sugimoto Spontaneous gravity wave radiation from nearly balanced rotational flows in a shallow water system
HRTW04 9th December 2008
14:00 to 14:30
Unusual properties of turbulent convection and dynamos in spherical shells
The dynamics of convecting fluids in rotating spherical shells is governed at Prandtl numbers of the order unity by the interaction between differential rotation and roll-like convection eddies. While the differential rotation is driven by the Reynolds stresses of the eddies, its shearing action inhibits convection and causes phenomena such as localized convection and turbulent relaxation oscillations. The response of the system is enriched in the case of dynamo action. Lorentz forces may brake either entirely or partially the geostrophic differential rotation and give rise to two rather different dynamo states. Bistability of turbulent dynamos exists for magnetic Prandtl numbers of the order unity. While the ratios between mean magnetic and kinetic energies differ by a factor of 5 or more for the two dynamo states, the mean convective heat transports are nearly the same. They are much larger than in the absence of a magnetic field.
HRTW04 9th December 2008
14:30 to 15:00
Angular momentum transport and dynamos in magnetised rotating stratified systems
In this presentation I shall discuss how the presence of a weak magnetic field may suppress the generation of large-scale zonal flows in stably stratified domains. I shall also discuss the characteristics of magnetic field generated via dynamo action in shallow-water magnetohydrodynamics
HRTW04 9th December 2008
16:00 to 16:30
Jet formation in decaying two-dimensional turbulence on a rotating sphere
Jet formation in decaying two-dimensional turbulence on a rotating sphere is reviewed from the view point of wave mean-flow interaction for both shallow-water case and non-divergent case as the limit of Fr (Froude number) going to zero. A series of computations are performed to confirm the behavior of zonal mean zonal flow generation on the parameter space of the rotation rate Omega and Fr. When the flow is non-divergent and Omega is large, intense retrograde circumpolar jets tend to emerge in addition to a banded structure of mean zonal flows with alternating flow directions. As Fr increases, circumpolar jets disappear and a retrograde jet emerges in the equatorial region. The appearance of the intense retrograde jets can be understood by the angular momentum transport associated with the generation, propagation, and absorption of Rossby waves. When the flow is non-divergent, long Rossby waves tend to be absorbed near the poles. In contrast, when Fr is large, Rossby waves can hardly propagate poleward and tend to be absorbed near the equator. The direction of the equatorial jet, however, is not always retrograde. Our ensemble experiments showed the emergence of a prograde jet, though less likely. This result is contrasted with the previous studies that reported retrograde equatorial jets in all the cases for shallow-water turbulence. Furthermore, a mean zonal flow induced by wave-wave interactions was examined using a weakly nonlinear model to investigate the acceleration mechanisms of the equatorial jet. The second-order acceleration is induced by the Rossby and mixed Rossby-gravity waves and its mechanisms can be categorized into two types.
HRTW04 9th December 2008
16:30 to 17:00
Magnetohydrodynamic shallow-water turbulence on the sphere
Motivated by astrophysical-geophysical applications, we have performed a series of high Reynolds number simulations of magnetohydrodynamic shallow-water turbulence (MHDSWT) on a rotating sphere. MHDSWT is the simplest turbulence model that allows the effects of differential rotation, stratification and magnetic field to be studied over long simulation times. A systematic exploration of the full physical and numerical parameter-space shows novel as well as consistent behavior, compared with those of pure hydrodynamic (HD) and 2-D MHD counterparts. In the case without rotation and weak magnetic field strength, the turbulent evolution is sensitive to initial conditions, with the strongest dependence on the peak of the initial energy spectrum. With increasing magnetic field strength, the flow field is more susceptible to loss of balance, and the field blows up in finite time. In addition, the pronounced zonal structures observed in differentially-rotating HD systems do not form.
HRTW04 10th December 2008
09:30 to 10:00
ME McIntyre Beyond Lighthill: three ways to stay close to balance
This talk proposes to discuss the recently discovered cases of hybrid propagating structures consisting of vortex dipoles and co-moving gravity waves undergoing wave capture. It is shown how these cases fall outside the scope of the Lighthill theory of spontaneous imbalance and, concomitantly, outside the scope of shallow-water dynamics. Besides the fact that going from shallow water to continuous stratification allows disparate vertical scales -- small for inertia-gravity waves and large for vortical motion -- the key points are (a) that in contrast with cases covered by the Lighthill theory the wave source in these cases feels an order-unity radiation reaction, hence cannot be prescribed in advance, when Rossby numbers R \sim 1; (b) that cases of this sort will supply exceptions to the general rule that spontaneous imbalance is exponentially small in R; and (c) that unsteady vortical motion in continuous stratification can stay close to balance thanks to three quite separate mechanisms. These are (1) the near-suppression, by Lighthill interference, of large-scale imbalance (inertia-gravity waves of large horizontal scale) where "large" means relative to Rossby deformation lengths L_D characterizing the vortical motion, (2) the low-group-velocity flaccidity hence near-steadiness of L_D-wide jets that meander and form loops, Gulf-Stream-like, on streamwise scales >> L_D, and (3) the dissipation of small-scale imbalance by wave capture leading to wave breaking, generically likely in an environment of random shear and straining. Shallow-water models include the first two mechanisms but exclude the third.
HRTW04 10th December 2008
10:00 to 10:30
J Vanneste Inertia-gravity-wave generation: a geometric-optics approach
The generation of inertia-gravity waves in complex flows is examined using a geometric-optics approach. This approach considers the dynamics of a small-scale wavepacket in prescribed time-dependent, balanced flow. The wavepacket is assumed to be in the so called wave-capture regime, where the wave intrinsic frequency is negligible compared with the Doppler shift. The dynamics is reduced to a number of ordinary differential equations describing the evolution of the wavepacket position, of the wavevector, and of three scalar fields describing the wavepacket amplitude and polarisation. The approach clearly identifies two classes of wave-generation processes: unbalanced instabilities, associated with linear interactions between inertia-gravity waves, and spontaneous generation, associated with a conversion between vortical and inertia-gravity modes. Applications to idealised and realistic flows are discussed.
HRTW04 10th December 2008
10:30 to 11:00
M Bustamante Dynamics of nonlinear resonance clusters in atmosphere and oceans
We regard as a starting point barotropic vorticity equation, for two types of boundary conditions: first, on a rotating sphere, second, in a rectangular basin. Our main goal is to study the dynamical systems describing small clusters of nonlinear resonances, the smallest one being a triad. For both types of boundary conditions, the geometrical and topological structures of the clusters are presented. It is shown that most frequently met clusters are integrable. It is also shown that dynamical phases, usually regarded as equal to zero or constants, play a substantial role in the dynamics of resonance clusters. Indeed, their effects are: (i) To reduce the period of energy exchange $\tau$ within a cluster by 20% and more. (ii) To diminish, at time scales of the order of $\tau$, the variability of wave energies by 25% and more. (iii) To generate a new time scale $T >> \tau$ in which we observe a considerable energy exchange within a cluster, as well as an increase in the variability of wave energies for each and every mode.
HRTW04 10th December 2008
11:30 to 12:00
Vortex simulations of 2D turbulence in confined domains
This talk considers the evolution of 2D turbulence in a confined domain with slip boundary conditions imposed. Several domain shapes are considered, both regular (e.g. a circle, a square) and irregular (e.g. random coastlines). The CASL (Contour-Advective Semi-Lagrangian) technique is employed, taking as the initial condition a random assembly of vortex patches. It is known that the initial angular momentum is important in determining whether the very long time state is dipolar or monopolar when no-slip boundary conditions are considered. Although this is not the case for slip boundary conditions, the initial total circulation plays a similar role. We explore the dependence of the final state on the initial circulation for a range of geometries. Some examples are shown where trapping of vortices in 'bays', caused by domain-scale interactions, can influence the long time evolution. Recent work on 2D turbulence in a periodic box has shown how the rate of dipole/monopole interactions can be related to the time rate of decay of enstrophy at intermediate to long times (once the initial very strong interactions are over). The presence of the domain boundary provides a mechanism for enhancing the rate of such interactions, as monopoles of opposite sign tend to hug the boundaries, travel in opposite directions and then meet to form dipoles which are then launched into the flow. Accordingly, we consider the effect of domain shape on the frequency of dipole formation and dipole/monopole interactions and the corresponding rate of decay of enstrophy. Finally, we discuss extensions of this work to the 3D quasi-geostrophic case.
HRTW04 10th December 2008
12:00 to 12:30
The hyper-CASL algorithm: an accurate, efficient new approach to modelling complex atmospheric and oceanic flows
We describe a powerful new approach to the simulation of layerwise-2D geophysical flows. Our approach combines the CASL algorithm, a hybrid contour-dynamics method ideally suited for the Lagrangian advection of potential vorticity (PV) contours across an Eulerian fixed grid, with a standard vortex-in-cell method. The latter is here used to compensate for errors arising from contour regularisation or surgery' appearing at the level of the grid. In this way, (essential) dissipation occurs only at sub-grid scales, and there is no direct impact of surgery on the computed velocity field, which is obtained on the grid by standard spectral or (compact) finite-difference methods. This is particularly important for long-term simulations, where error accumulation needs to be minimised. This new approach, coined the hyper-CASL algorithm', also allows for general non-conservative effects, by design. For instance, one may take account of radiative (thermal) effects which attract a given flow to some thermal equilibrium distribution, or one can account for Ekman pumping' which converts wind stress at the ocean's surface into a vorticity source or sink there. In fact, very general forms of forcing or damping can be accounted for (e.g. stochastic, moisture, small-scale convection, etc.). Hyper-CASL is not limited to PV, but can be applied to other tracers such as chemical species in the atmosphere, including moisture. In particular, modelling water vapour by contours and subgrid-scale convection by Lagrangian particles may be a timely opportunity to improve the forecasting of precipitation. Hyper-CASL is illustrated here in long-term simulations of quasi-geostrophic and shallow-water turbulence. These simulations reveal unprecedented detail, in particular vortices spanning a very wide range of scales and significantly affecting flow statistics.
HRTW04 11th December 2008
09:30 to 10:00
GK Vallis Is geostrophic turbulence relevant for tropospheric dynamics?
Geostrophic turbulence is a model for understanding the large-scale structure and flow of energy in stably-stratified, rapidly rotating flows that, typically, are baroclinically unstable or driven externally by small-scale convection. Inverse energy cascades and the production of zonality by the beta effect robust predictions for such flows. Is such a model relevant for the Earth's troposphere? On the one hand it appears that such a model must surely be relevant because of its generality, but on the other hand the inverse cascade is noticeable by its absence in the Earth's atmosphere, and zonal jets do not appear as well formed as those on some other planets. We will discuss these issues, and compare some turbulent simulations from a quasi-geostrophic model with those from a primitive-equation model in parameter settings including, but not restricted to, the Earth's troposphere. Joint work with P. Zurita-Gotor.
HRTW04 11th December 2008
10:00 to 10:30
Spectral study of stably stratified turbulence
The energy spectrum of stably stratified turbulence is studied numerically by solving the 3D Navier-Stokes equations under the Boussinesq approximation pseudo-spectrally. The resolution is $1024^3$. Using toroidal-polodial decomposition (Craya-Herring decomposition), the velocity field is divided into the vortex mode and the wave mode. For randomly forced flows, we show that there is a sharp wave number transition in the energy spectra of the vortex and wave modes. With the initial kinetic energy zero, the vortex-mode first develop a $k_{¥perp}^{-3}$ spectrum for the whole wavenumber range studied. Here, $k_{¥perp}¥equiv ¥sqrt{k_x^2+k_y^2}$. Then at large $k_{¥perp}$, a $k_{¥perp}^{-5/3}$ part appears with a sharp transition in the wave number. Meanwhile the wave-mode spectra show a $k_{¥perp}^{-2}$ first, and then $k_{¥perp}^{-5/3}$ part appears at high $k_{¥perp}$. Spectra for different values of the Brunt-Vaisala frequency are investigated. We present evidence that the $k_{¥perp}^{-3}$ part at the large scale in the vortex-mode spectra may be characterized as 2d turbulence. The small scale part is a Kolmogorov spectrum $¥sim ¥epsilon^{2/3}k_{¥perp}^{-5/3}$, where $¥epsilon$ is the horizontal energy dissipation of the vortex-mode. Finally, we discuss decaying stratified turbulence. We note that our present high resolution simulations support earlier simulations (Kimura & Herring 1996) in which the decay of total energy was found to be $E(t)¥sim t^{-1}$. An explanation for such a decay is proposed in terms of the shape of the toroidal and polodial energy spectra.
HRTW04 11th December 2008
10:30 to 11:00
S Nazarenko Triple cascade and zonal flows in beta-plane turbulence
At low amplitudes, the beta-plane model has three conservation laws: the energy, the potential enstrophy and the zonostrophy (an additional invariant found by Balk, Nazarenko and Zakharov in 1991). Application of a standard Fjortoft argument to this system leads to a conclusion that these 3 invariants must cascade in an anisotropic fashion, each cascade occupying its own sector in the 2D k-space. It appears that the energy cascade sector corresponds to generation of large-scale zonal flows in the system. I will discuss some recent numerics aimed at checking conservation of zonostrophy and the triple cascade property.
HRTW04 11th December 2008
11:30 to 12:00
T Miyazaki Equilibrium state of quasi-geostrophic point vortices
The statistics of quasi-geostrophic point vortices is investigated theoretically and numerically, in order to understand fundamental aspects of quasi-geostrophic turbulence. Numerical simulations of N-vortex system (N = 2000 − 8000) in an infinite fluid domain are performed using a fast special-purpose computer (MDGRAPE-3) for molecular dynamics simulations.[1] The vortices of the same strength are initially located randomly and uniformly in a cubic box, and we choose the state with the highest multiplicity for fixed angular momentum. The axi-symmetric equilibrium state is obtained after about 20 turn over time. The probability density distribution of the center region resembles that of the purely two-dimensional point vortices. The three-dimensional effect appears near the upper and lower lids in the tighter concentration of vortices around the axis of symmetry (End-effect). The most probable vortex distributions are determined based on the maximum entropy theory.[2] We search for the state of maximum Shanon-entrophy under the constraints of vertical vorticity distribution, angular momentum and energy (mean-field approximation). The theoretical predictions agree quite well with the numerical results.[3] We investigate the influence of energy on the equilibrium state, in some detail. Larger vortex clouds have lower energy, larger entropy and lager angular momentum. Each vertical layer has same contribution to the entropy and the angular momentum, whereas the center region has stronger influence to the energy than the lids. Therefore, the distribution in the center region expands radially for lower energy and shrinks for higher energy. In order to keep the angular momentum unchanged, the distribution near the lids should shrink for lower energy and should expand for higher energy. References [1] Yatsuyanagi Y., Kiwamoto Y., Tomita H., Sano M.M., Yoshida T., Ebisuzaki. T.: Dynamics of Two-Sign Point Vortices in Positive and Negative Temperature States. Phys. Rev. Lett. 94:054502, 2005 [2] Kida S.: Statistics of the System of Line Vortices. J. Phys. Soc. Jpn. 39(5):1395–1404, 1975 [3] Hoshi S., Miyazaki T.: Statistics of Quasi-geostrophic Point Vortices. FDR (Subbmitting), 2008.
HRTW04 11th December 2008
12:00 to 12:30
Influence of external shear and strain on baroclinic vortex alignment
The influence of an external strain (or shear) field on the evolution of two identical vortices at different depths is investigated in a two-layer quasi-geostrophic model. The external deformation can include a time-varying component. Using point vortex modeling, symmetric equilibrium positions for the vortex doublet are identified and their stability is computed. A time- varying external field can induce resonances on both harmonic and subharmonic frequencies. A slow time amplitude equation is then computed for the vortex trajectories around their equilibrium positions ; its solutions are compared successfully to numerical simulations of a baroclinic point vortex model. The evolution from regular to chaotic trajectories when the external field amplitude grows, is analyzed. Finite-area vortices exhibit the classical regimes of alignment or of co-rotation when submitted to external strain and rotation, but they can also remain stationary at the location of the neutral points for the equivalent point vortices, or oscillate around these positions. Another regime is evidenced, in which originally very distant vortices are advected towards the center of the plane by the large-scale flow, and finally merge. Thus, in a dense field of coherent structures, neighboring vortices can favor the vertical alignment of two central vortices, despite the erosion that they induce on these vortices.
HRTW04 11th December 2008
14:00 to 14:30
J Herring Spectra and distribution functions of stably stratified turbulence
We consider homogeneous stably stratified turbulence both decaying and randomly forced cases. Our tools include direct numerical simulations (DNS) and elements of statistical theory as expressed by two-point closures. Our DNS--at $1024^3$--permits a large scales Taylor micro scale $R_{\lambda}\sim 300$ The size distribution of such large scales is closely related to conservation principles, such as angular momentum, energy, and scalar variance; and we relate these principles to our DNS results. Stratified turbulence decays more slowly than isotropic turbulence with the same initial conditions. We offer a simple explanation in terms of the diminution of energy transfer to small scales resulting from phase-mixing of gravity waves (Kaneda 1998). Enstrophy structures in stratified flows (scattered pancakes) are distinctly different from those found from isotropic turbulence (vortex tubes), and we show examples of the transition from isotropic turbulence enstrophy structures to those of strongly stratified turbulence. We discuss briefly changes in the probability distribution functions for velocity and vorticity for stratified turbulence concluding that stratification induces a return towards Gaussianity for these quantities. For the forced case, we examine the modification of the inertial range induced by strong stratification ($k_{\perp}^{-5/3}\rightarrow \sim k_{\perp}^{-2}$) for the wave component, and ($k_{\perp}^{-5/3}\rightarrow\sim k_{\perp}^{-3}$) for the vortical component. Here, $k_{\perp}$ is the horizontal wave number. These DNS findings are discussed from the perspective of two-point closure.
HRTW04 11th December 2008
14:30 to 15:00
Stratified turbulence: a possible interpretation of some geophysical turbulence measurements
Stratified turbulence is a flow dominated by stable density stratification, and characterized by low internal Froude numbers and high Reynolds numbers; in the present study it is also assumed that the Rossby number is large. Flows in such parameter regimes occur often in the oceans and in the atmosphere. Results of direct numerical simulations of stratified turbulence, some scaling arguments, and implications regarding laboratory experiments will be presented. The results suggest that stratified turbulence is a possible interpretation of some oceanic and atmospheric measurements.
HRTW04 11th December 2008
16:00 to 16:30
Once again about the parallel between stratification and rotation in hydrodynamics and between both and external magnetic field in MHD
On the example of simplified 2D models I will discuss the mathematical background of the well-known parallel between the effects of stratification, rotation and external magnetic field. Special emphasis will be made on the fact that Hamiltonian structure of the corresponding hydrodynamical systems is the same, and the consequences of this fact in what concerns both the coherent structures (stationary nonlinear waves/vortices) and the equilibrium spectra of wave turbulence of anisotropic waves proper to each effect (internal gravity waves, gyroscopic waves, and Alfven waves, respectively)
HRTW04 11th December 2008
16:30 to 17:00
Application of statistical mechanics to the modeling of potential vorticity or density mixing
Statistical mechanics of vortex patches can provide models for potential vorticity mixing with the constraints of fluid incompressibility and energy conservation. This leads to the self-organisation of turbulence into large coherent structures. We can apply a similar approach to the vertical mixing of fluid elements with different densities. This leads to a model of vertical mixing which involves the competition of an eddy diffusivity with sedimentation of fluid elements. In addition to these two processes, the straining of fluid elements by eddies must be included. The behaviour of the resulting model will be discussed for different cases of vertical mixing in a stratified fluid.
HRTW04 12th December 2008
09:30 to 10:00
Bounds on the energetics and entropy production of a buoyancy forced ocean
We show that the volume averaged rate of entropy production in horizontal convection, i.e., $\chi \equiv \kappa$ where $b$ is the buoyancy, is bounded from above by $4.57 H^{-1} \kappa^{2/3} \nu^{-1/3} b_{\rm max}^{7/3}$. Here $H$ is the depth of the container, $\kappa$ is the molecular diffusion, $\nu$ the kinematic viscosity and $b_{\rm max}$ the maximum buoyancy difference prescribed on the surface. The rate of entropy production is directly related, via the volume integrated diapycnal buoyancy flux, to the energetics of irreversible mixing and the rate of energy transfer between available and background potential energy in the Boussinesq limit. The bound implies that the rate of generation of available potential energy by horizontal convection is no larger than $\kappa^{1/3}$ in the limit $\kappa \to 0$ at fixed $Pr=\nu/\kappa$. The bound on the energetics of mixing reinforces and strengthens the statement of Paparella and Young (2002) that horizontal convection is nonturbulent in limit of vanishing fluid viscosity and diffusivity. In the context of a model ocean, insulated at all boundaries except at the upper surface where the buoyancy is prescribed, the bounds on the energy transfer rates in the mechanical energy budget imply that buoyancy forcing alone is insufficient by at least three orders of magnitude to maintain observed or inferred average oceanic dissipation rates and that additional energy sources such as winds, tides or (perhaps) bioturbation are necessary to sustain nontrivial levels of turbulent dissipation and mixing in the world's oceans
HRTW04 12th December 2008
10:00 to 10:30
Simulations of stratified turbulence surrounding Meddy structures
Recently available geosismic data in the North-East Atlantic ocean have revealed ubiquituous pancake-like layers of density anomalies of 30-60 meters thickness, surrounding Meddy structures within the Mediterranean Water outflow. The depths of pancake-like density layering unambiguously coincide with potential energy spectra in $k_h^{-5/3}$,-- where $k_h$ is the horizontal wavenumber--, for horizontal spatial scales less than 1km, reminiscent of non-rotating stratified turbulence results. Using ultra-high 3D resolution simulations of a Meddy structure on the Earth Simulator, with a horizontal grid size down to 100m and a vertical grid size of 3m, we have been able to reproduce the pancake-like layering surrounding the eddy. Furthermore, potential and kinetic energy with $k_h^{-5/3}$ inertial ranges are simulated. A rationale is proposed for the formation mechanism of the layering and we discuss the influence of rotation on stratifed turbulence properties.
HRTW04 12th December 2008
10:30 to 11:00
Internal tide generation from surface tide/geostrophic Eddy interactions
Most studies of internal tide generation have focused on the role of the barotropic tide interacting with topography. Our study focuses on a mechanism which has not been considered up to now, namely the interaction of a barotropic tide with a baroclinic eddy field. The interaction of a barotropic tidal current and a mesoscale eddy field is investigated to determine the ambient conditions under which energy is transferred most efficiently from barotropic to baroclinic tides. We examine the transfer of energy as a function of latitude and eddy field structure. The existence of critical latitudes is also discussed in this context.
HRTW04 12th December 2008
11:30 to 12:00
Propagation of the internal tide from a continental shelf: laboratory and numerical experiments
Internal gravity waves in the deep ocean have been given much importance for the last ten years, since oceanographers realized the important role of fluid mixing in raising the cold abyssal water masses. Mixing in the deep ocean, below 2 or 3 kms, is indeed thought to be mostly due to nonlinear internal gravity waves. In the abyss, internal waves result mainly from the interaction of the surface tide with the variable bottom topography and are referred to as the internal tide. The thermal equilibrium of the deep ocean thus depends upon local and strongly intermittent processes -the breaking internal tide- which occur on temporal scales of the order of one minute and on spatial scales of the order of ten meters. This gigantic difference in spatial and temporal scales requires the parameterization of the mixing processes in large scale circulation models. A direct study of the breaking internal tide is therefore needed. The present study focuses upon the academic situation of a uniformly stratified ocean, when the surface tide interacts with an idealized two-dimensional continental shelf. Numerical experiments have been conducted in close correspondance with the laboratory experiments, the geometrical and physical parameters being the same. The laboratory experiments have been performed on the rotating Coriolis platform in Grenoble. The nonlinear non-hydrostatic finite-volume numerical code developed at MIT was used to closely model the experiments. In this simplified situation, the internal wave field organizes as a rectilinear wave beam with tidal frequency. We shall discuss the generation mechanism and structure of the wave beam, relying on theoretical modelling of internal wave emission by an oscillating body source. We shall also investigate the nonlinear dynamics of the tide, when harmonics and parametric sub-harmonics are generated. The localization and quantification of mixing induced by the internal tide will eventually be considered.
HRTW04 12th December 2008
12:00 to 12:30
2d-3d energy exchanges in a homogeneous thin-aspect-ratio ocean
Because of its thin aspect ratio, large scale ocean circulation is generally assumed to obey hydrostatic dynamics. In the idealized case of a homogeneous (unstratified) fluid, this implies that the horizontal pressure gradient force is independent of depth. Homogeneous models of ocean circulation typically assume the flow to be two dimensional. However, it can be shown that such a two dimensional flow is unstable to 3d perturbations. Following saturation of the 3d perturbations, a 2d-to-3d energy transfer persists. After a brief description of the instability mechanism, we i) test its robustness to nonhydrostatic effects and ii) address its potential role in the damping of midlatitude ocean gyres. Initially 2d turbulence in a Boussinesq fluid is shown numerically to be unstable to 3d perturbations. Although non-hydrostatic pressure effects act to slow the growth, a robust growth in nonetheless observed even at unit aspect ratio. The perturbations are found to saturate at a level proportional to the domain aspect ratio. Thus, in the thin aspect ratio limit, nearly 2d dynamics are recovered --- provided the 3d modes are not externally forced. We then consider the classic wind-driven ocean gyre problem for a homogeneous thin aspect ratio fluid on a beta plane. A large-scale stochastic forcing is applied to the 3d modes. This produces a background sea of near-inertial oscillations which interact with the depth averaged flow. It is found that 2d-to-3d energy transfers coupled with a forward cascade of 3d energy provides a robust dissipation mechanism for the gyres. We speculate that similar dynamics may also apply in a stratified ocean.
HRTW04 12th December 2008
14:00 to 14:30
Richardson number-dependent bounds on buoyancy flux
Parameterizing the mixing of a stratified fluid subject to shear is a fundamental challenge for models of environmental and industrial flows. In particular, it is of great value to parameterize the efficiency of turbulent mixing, in the sense of the proportion of the kinetic energy converted into potential energy (through irreversible mixing of fluid of different density) compared to the total amount converted to both potential energy and internal energy (through viscous dissipation). Various competing models have been presented to relate the mixing efficiency to bulk properties of the flow, especially through different Richardson numbers, which quantify the relative importance of buoyancy and shear within the flow. One promising approach is to construct rigorous bounds on the long-time average of the buoyancy flux (i.e. the mixing rate) within simple model stratified shear flows, imposing physically reasonable constraints on the model flow fields. In this talk, we apply this technique to stably stratified Couette flow, imposing as a constraint the mixing efficiency, and show that a bound on the long-time average of the buoyancy flux can only be found for a certain range of bulk Richardson numbers. For sufficiently strong stratifications, it appears that no bound exists, suggesting that it is not possible to find a statistically steady state. We discuss the implications of this result for various classical stratified shear turbulence models.
HRTW04 12th December 2008
14:30 to 15:00
JM Chomaz Three-dimensional stability of a horizontally sheared flow in a stably stratified fluid
This work investigates the three-dimensional stability of a horizontal flow sheared horizontally, the hyperbolic tangent velocity profile, in a stably stratified fluid. In an homogeneous fluid, the Squire theorem states that the most unstable perturbation is two-dimensional. When the flow is stably stratified, this theorem does not apply and we have performed a numerical study to investigate the three-dimensional stability characteristics of the flow. When the Froude number, Fh, is varied from ∞ to 0.05, the most unstable mode remains two-dimensional. However, the range of unstable vertical wavenumbers widens proportionally to the inverse of the Froude number for Fh 1. This means that the stronger the stratification, the smaller the vertical scales that can be destabilized. This loss of selectivity of the two-dimensional mode in horizontal shear flows stratified vertically may explain the layering observed numerically and experimentally. Extension to transient and nonlinear behaviour are presented.
HRT 15th December 2008
10:00 to 11:00
Homogeneous three-dimensional rotating flows, intertial waves and turbulence
HRT 15th December 2008
11:30 to 12:30
Rotating turbulence
HRT 16th December 2008
15:00 to 16:00
Stratified turbulence