# Seminars (SIP)

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Event When Speaker Title Presentation Material
SIP 5th September 2017
15:00 to 16:30
Current topics on sea-ice research: Led by A Korobkin
Several participants of the Programme will speak about their areas of expertise, current interests in ice research, and possible cooperation within the Programme. The seminar is led by A. Korobkin

SIP 6th September 2017
15:00 to 16:30
Erick Rogers Dissipation of wind waves by pancake and frazil ice in the autumn Beaufort Sea
I will be presenting the following paper:
W.E. Rogers, J. Thomson, H.H. Shen M.J. Doble, P. Wadhams and S. Cheng, 2016:
Dissipation of wind waves by pancake and frazil ice in the autumn Beaufort Sea
Journal of Geophysical Research: Oceans vol 121 7991-8007 doi:10.1002/2016JC012251
The full paper may be found at the link above.
The abstract follows:
A model for wind-generated surface gravity waves, WAVEWATCH III (R), is used to analyze and interpret buoy measurements of wave spectra. The model is applied to a hindcast of a wave event in sea ice in the western Arctic, 11–14 October 2015, for which extensive buoy and ship-borne measurements were made during a research cruise. The model, which uses a viscoelastic parameterization to represent the impact of sea ice on the waves, is found to have good skill—after calibration of the effective viscosity—for prediction of total energy, but over-predicts dissipation of high frequency energy by the sea ice. This shortcoming motivates detailed analysis of the apparent dissipation rate. A new inversion method is applied to yield, for each buoy spectrum, the inferred dissipation rate as a function of wave frequency. For 102 of the measured wave spectra, visual observations of the sea ice were available from buoy-mounted cameras,and ice categories (primarily for varying forms of pancake and frazil ice) are assigned to each based on the photographs. When comparing the inversion-derived dissipation profiles against the independently derived ice categories, there is remarkable correspondence, with clear sorting of dissipation profiles into groups of similar ice type. These profiles are largely monotonic: they do not exhibit the ‘‘roll-over’’ that has been found at high frequencies in some previous observational studies.

The introduction to the seminar will include a general overview of wave forecasting for the Arctic.
Public release statement: The published paper has been approved for public release. The introduction/overview slides are pulled from earlier presentations which were approved for public release.
SIPW01 11th September 2017
09:45 to 10:30
Donald K. Perovich Small to big, quick to slow: The many scales of sea ice properties and processes
Sea ice properties and processes exhibit tremendous variability over spatial scales from millimeters to megameters. Sea ice also evolves over temporal scales of hours to days to seasons to decades. To understand sea ice properties, it is critical to examine and connect the processes that occur on these different scales. For example, sea ice microstructure impacts the partitioning of sunlight. Melt ponds are governed by meter-scale topography and millimeter-scale brine channels. There are similarities in the size distributions of brine pockets, melt ponds, and floes; features that span spatial scales of several orders of magnitude. The timing of short term events, such as snowfall or lead openings, has a large impact on the seasonal evolution of the ice cover. Sea ice scale issues are also important when considering the interactions of the atmosphere-sea ice-ocean-biogeochemical system.
SIPW01 11th September 2017
11:00 to 11:45
Ken Golden Linking scales in the sea ice system
Sea ice exhibits complex structure ranging from the sub-millimeter scale brine inclusions to ice floes and coherent​ ​dynamics on the scale of hundreds of kilometers. I will give an overview of how we are using​ ​ theories of composite​ materials and statistical physics to link behavior on various scales in the sea ice system. In particular, we address key questions in sea ice homogenization, where information on smaller scales is incorporated into rigorous representations of effective large scale behavior. We also consider the inverse problem where small scale structure is inferred from larger scale effective properties.
SIPW01 11th September 2017
11:45 to 12:30
Agnieszka Herman Discrete-element models of sea ice dynamics and fracture
At geophysical scales, continuum models provide established and computationally efficient tools for simulating sea ice dynamics and thermodynamics. In recent years, rapidly increasing computational power and availability of high-resolution (esp. remote-sensing) data have contributed to a revival of discrete-element methods (DEM), enabling the analysis of sea ice at smaller spatial and temporal scales. Treating sea ice as a collection of individual, interacting floes, and thus recognizing it as an example of a granular material, opens a wide range of new tools and analysis possibilities for sea ice research. Bonded-particle DEM models enable to simulate brittle fragmentation of sea ice – a process that, in spite of substantial progress in recent years, still poses problems for continuum models. Moreover, there is growing evidence that the size distribution of sea ice floes has a substantial influence on a wide range of processes in the upper ocean, lower atmosphere and within sea ice itself, and it is in turn shaped by those processes. By directly taking into account fragmentation (i.e., floe formation) and dynamics of individual floes, DEMs provide tools to better understand complex interactions between sea ice, ocean and atmosphere acting at the floe-level.

In this talk, I will present and discuss selected examples of the application of DEM models to sea ice dynamics and fragmentation problems. The examples will include: wind- and current-induced drift of fragmented (granular’’) sea ice, and the influence of ice concentration and floe-size distribution on the sea ice response to forcing; jamming phase transition under compressive and shear strain, and force transmission in ice subject to different strain fields; sea ice breaking by waves analyzed with a coupled DEM–hydrodynamic model. Unsolved problems and challenges (both computational and theoretical) related to the application of DEMs to sea ice will be presented as well.

Most results presented in this talk were obtained with a Discrete-Element bonded-particle Sea Ice model DESIgn, implemented as a toolbox for the open-source numerical library LIGGGHTS (http://www.cfdem.com/). The code and documentation of DESIgn are freely available at http://herman.ocean.ug.edu.pl/LIGGGHTSseaice.html.

SIPW01 11th September 2017
14:00 to 14:30
Veronique Dansereau A new continuum rheological model for the deformation and drift of sea ice
Co-authors: Pierre Saramito (CNRS-LJK), Jérôme Weiss (CNRS-ISTerre), Philippe Lattes (Total S.A. E&P)

Axel Roy (1)
Véronique Dansereau (2)*
Jérôme Weiss (2)
Christian Haas (3)
Matthieu Chevalier (4)

1 École Nationale de la Météorologie, Météo France, Toulouse, France
2 Institut des Sciences de la Terre, CNRS UMR 5275, Université de Grenoble, Grenoble, France
3 Alfred Wegener Institute, Bremerhaven, Germany
4 CNRM/GMGEC/IOGA Météo France, Toulouse, France

Sea ice models are most often compared to each other and to observations in terms of the spatial distribution of the simulated ice thickness. An equally important, and perhaps more appropriate, metric to investigate the mechanical behaviour of the sea ice cover is the ice thickness distribution, i.e., the probability density function, of which some valuable information have been available for some time from drill-hole, upward looking submarine-mounted sonar (USL) and airborne electromagnetic (EM) sounding measurements.

An important issue naturally arises when comparing sea ice thickness distributions based on measurements made at the meter scale with that estimated from regional and global sea ice model simulations, with a typical resolution of a few kilometres; the issue of scale dependance. Using USL sea ice draft profiles and EM thickness measurements, we investigate the scaling properties of the sea ice thickness over the Arctic to address the following question: how does the sea ice thickness distribution evolve with the scale of observation?

The autocorrelation calculations performed here allow extending previous analyses based on single USL transects (up to 50 km-long) and point to long-range correlations in the thickness of the sea ice cover reaching as far as a few hundreds of kilometres. Multi-fractal analyses are conducted to investigate the variability of the the ice thickness distribution with the spatial scale of observation up to these scales.
SIPW01 11th September 2017
14:30 to 15:00
Christopher Horvat Floe size and ice thickness distributions
SIPW01 11th September 2017
15:30 to 16:00
Courtenay Strong Filling the polar data gap with harmonic functions
Coauthors: Elena Cherkaev and Kenneth M. Golden

The “polar data gap” is a region around the North Pole where satellite orbits do not provide sufficient coverage for estimating sea ice concentrations. This gap is conventionally made circular and assumed to be ice-covered for the purpose of sea ice extent calculations, but recent conditions around the perimeter of the gap indicate that this assumption may already be invalid. We present partial differential equation-based models for estimating sea ice concentrations within the area of the data gap. In particular, the sea ice concentration field is assumed to satisfy Laplace’s equation with boundary conditions determined by observed sea ice concentrations on the perimeter of the gap region. This type of idealization in the concentration field has already proved to be quite useful in establishing an objective method for measuring the “width” of the marginal ice zone—a highly irregular, annular-shaped region of the ice pack that interacts with the ocean, and typically surrounds the inner core of most densely packed sea ice. Realistic spatial heterogeneity in the idealized concentration field is achieved by adding a spatially autocorrelated stochastic field with temporally varying standard deviation derived from the variability of observations around the gap. Testing in circular regions around the gap yields observation-model correlation exceeding 0.6 to 0.7, and sea ice concentration mean absolute deviations smaller than 0.01. This approach based on solving an elliptic partial differential equation with given boundary conditions has sufficient generality to also provide more sophisticated models which could be more accurate than the Laplace equation version, and such potential generalizations are explored.
SIPW01 11th September 2017
16:00 to 17:00
Elizabeth Hunke Rothschild Lecture: Large-scale sea ice modeling: societal needs and community development
The CICE sea ice model is used extensively by climate and Earth system research groups, and also by operational centers for applications such as numerical weather prediction and guidance for military operations.  While the research community is energetically improving the models, observationalists are busy taking measurements and operational experts are using all of it to produce predictive products via data assimilation.  In the past, the sea ice research and operational communities have been somewhat distinct with little cross-pollination.  Partly in response to this issue, the CICE Consortium has formed as a formal community effort to to provide a mechanism for accelerating further sea ice model development and its transfer into operational uses.  This colloquium will provide a broad overview of current CICE model capabilities and uses, highlight new analysis techniques for statistically assessing model skill against diverse observations, and discuss our community engagement effort, all toward addressing society's needs in the face of the Earth’s changing polar regions.

SIPW01 12th September 2017
09:00 to 09:45
Vernon Squire Marginal Ice Zone Evolution due to Wave-Induced Breaking
Co-authors: Vernon Squire (University of Otago, NZ), Fabien Montiel (University of Otago, NZ)

The influence of ice–albedo temperature feedback arising as a result of global climate change is believed to be enhanced by a contemporaneous intensification of wave climate in the polar seas. Waves break up the sea ice deeper into the ice-covered oceans, accelerating its melting and increasing the area of ice-free ocean, which in turn allows for more energetic waves and swells to develop. Although much attention has been given to the effect of a broken-up ice cover, e.g. the marginal ice zone, on the propagation of ocean waves, less is known about the impact of waves on the morphology of the sea ice. The latter is principally governed by the break-up of flexing sea-ice floes as a result of wave interactions. A sub-grid scale process-based model describing the two-way coupling between the ocean waves and sea ice systems will be discussed, with a particular focus on how to parametrize this coupling in ice/ocean models.
SIPW01 12th September 2017
09:45 to 10:30
Martin Vancoppenolle A compilation of research and thoughts on the future of sea ice models.
On the point of view of a model developer, it looks somehow desperating to see how little sensitive climate models seem to be to the representation of sea ice processes. By comparison, atmospheric and oceanic forcing, or mean climate state look much more influential. Is this a good reason to give up sea ice model development ? I will give a few elements of answer to explain why we should maintain our efforts, and illustrate how the European teams involved in NEMO will project themselves into the next generation of sea ice models.
SIPW01 12th September 2017
11:00 to 11:45
Daniel Feltham Sea ice model physics: in search of fidelity
SIPW01 12th September 2017
11:45 to 12:30
Wieslaw Maslowski Sensitivity of Arctic sea ice state to model parameter space, resolved processes and climate coupling
SIPW01 12th September 2017
14:00 to 14:30
Sukun Cheng A viscoelastic model for wave propagation in the marginal ice zone
Co-author: Hayley H. Shen (Clarkson Univerisity)

Regional wave forecasts for the Arctic rely on a good understanding of wave propagation through sea ice covers. Disagreements among the models and the lack of field validations cause uncertainty in wave forecasts. A recent viscoelastic ice model has been developed to simulate a wide range of ice covers. This model synthesized several previous models that considered ice covers as a continuum. In this model, a simple parameterization is used to include both energy storage and dissipation mechanisms. However, the model has two parameters, the equivalent elasticity and viscosity, which need to be determined. In this presentation, we will describe the basis of this model, and its calibration using data from a recent field campaign.
SIPW01 12th September 2017
14:30 to 15:00
Christian Samspon Effective Rheology and Wave Propagation in the Marginal Ice Zone
Co-authors: Ken Golden (University of Utah), Ben Murphy (University of Utah), Elena Cherkaev (University of Utah)

Wave-ice interactions in the polar oceans comprise a complex but important set of processes influencing sea ice extent, ice pack albedo, and ice thickness. In both the Arctic and Antarctic, the ice floe size distribution in the Marginal Ice Zone (MIZ) plays a central role in the properties of wave propagation. Ocean waves break up and shape the ice floes which, in turn, attenuate various wave characteristics. Recently, continuum models have been developed which treat the MIZ as a two-component composite of ice and slushy water. The top layer has been taken to be purely elastic, purely viscous or viscoelastic. At the heart of these models are effective parameters, namely, the effective elasticity, viscosity, and complex viscoelasticity. In practice, these effective parameters, which depend on the composite geometry and the physical properties of the constituents, are quite difficult to determine. To help overcome this limitation, we employ the methods of homogenization theory, in a quasistatic, fixed frequency regime, to find a Stieltjes integral representation for the complex viscoelasticity.
This integral representation involves the spectral measure of a self adjoint operator and provides what we believe are the first rigorous bounds on the effective viscoelasticity of the sea ice pack. The bounds themselves depend on the moments of the measure which in turn depend on the geometry of the ice floe configurations. This work has the potential to provide simple parameterizations of wave properties which take into account floe concentration and geometry.
SIPW01 12th September 2017
15:30 to 16:00
Co-author: Jörn Behrens (University of Hamburg, Germany)

Simulation over a long time scale in climate sciences as done, e.g., in paleo climate simulations require coarse grids due to computational constraints. Unresolved scales, however, significantly influence the coarse grid variables. Such processes include (slowly) moving land-sea interfaces or ice shields as well as flow over urbanic areas. Neglecting these scales amounts to unreliable simulation results. State-of-the-art dynamical cores represent the influence of subscale processes typically via subscale parametrizations and often employ heuristic coupling of scales.

Our aim is to improve the mathematical consistency of the upscaling process that transfers information from the subgrid to the coarse prognostic scale (and vice-versa). We investigate a new bottom-up techniques for advection dominated problems arising in climate simulations [Lauritzen et al. (2011)]. Our tools are based on ideas for multiscale finite element methods for elliptic problems that play a role in oil reservoir modeling and porous media in general [Efendiev and Hou (2009), Graham et al. (2012)]. Modifying these ideas is in necessary in order to account for the transient and advection dominated character which is typical for flows encountered in climate models.

We present a new Garlerkin based idea to account for the typical difficulties in climate simulations. Our modified ideas employ a change of coordinates based on a coarse grid characteristic transform induced by the advection term in order to account for appropriate subgrid boundary conditions for the multiscale basis functions which are essential for such approaches. We present results from sample runs for a simple advection-diffusion equation with rapidly varying coefficients on several scales.
SIPW01 12th September 2017
16:00 to 16:30
Noa Kraitzman Advection enhanced diffusion processes
We investigate thermal conduction in sea ice in the presence of fluid flow, as an important example of an advection diffusion process in the polar marine environment. Using new Stieltjes integral representations for the effective diffusivity in turbulent transport, we present a series of rigorous bounds on the effective diffusivity, obtained using Padé approximates in terms of the Péclet number.
We first analyze the effective thermal conductivity of sea ice in the presence of an averaged convective velocity field, neglecting the two phase microstructure of sea ice, and then present a homogenization analysis of the full two component system composed of brine and ice.
SIPW01 13th September 2017
09:00 to 09:45
Ian Eisenman Sea ice stability and rapid retreat
Changes in the Arctic sea ice cover involve an amplifying feedback associated with the surface albedo, which suggests the possibility of unstable climate states and bifurcations, or "tipping points". The first part of this talk will focus on the stability of the sea ice cover. Previous studies have identified sea ice bifurcations due to the ice-albedo feedback occurring in a range of idealized models but not in comprehensive global climate models (GCMs). We will propose a physical explanation for this discrepancy, drawing on a model that we developed to bridge the gap between low-order models and GCMs. The results support the finding from GCMs, suggesting that such bifurcations should not be expected in nature. Nonetheless, Arctic sea ice has been observed to retreat abruptly during recent decades. The second part of the talk will address how well the observed rate of Arctic sea ice retreat is simulated in the suite of current GCMs. Although the majority of these GCMs simulate less sea ice retreat than observed, a substantial minority of the simulations do capture the observed rate of retreat. Hence a number of recent studies have suggested that the GCMs and the observations are consistent. We will show that the observed rate of Arctic sea ice retreat actually occurs only in GCM simulations with substantially more global warming than observed. We will suggest an alternative metric for evaluating the GCMs that takes this factor into consideration. The results suggest that the GCMs may be getting the right Arctic sea ice trends for the wrong reasons.
SIPW01 13th September 2017
09:45 to 10:30
Andrew Roberts Modeling macro-porosity of ridged sea ice in basin-scale models
Co-authors: Elizabeth Hunke (Los Alamos National Laboratory), William Lipscomb (National Center for Atmospheric Research), Samy Kamal (Naval Postgraduate School), Wieslaw Maslowski (Naval Postgraduate School)

One of the largest limitations of current-generation sea ice models is that they characterize sea ice morphology using a thickness distribution, g(h), over an area A(x). This inherently introduces a scale limitation to sea ice models, because g(h) only represents the relative quantity of ice of thickness, h, over a region, rather than describe how thickness is locally organized. Moreover, the approach assumes that sea ice deformed into rafts, folds, buckles, ridges and hummocks is equally as porous as undeformed ice, despite strong evidence to the contrary. This problem may be addressed by expanding the state space of the thickness distribution to become a multivariate distribution g(h,phi) where phi is the macro-porosity of sea ice rubble. Then, sea ice ridging may be described using a Euler-Lagrange equation for ridge cross-sections that mimic many of the characteristics of existing ridge-scale simulations. The approach requires careful consideration of non-conservative components of ridging, and, in the most basic approach, can use a Coulombic failure criteria applied vertically within ridges to predict their angle of repose, macro-porosity, extent and seperation in large scale models. This talk presents the theoretical basis for this new method of simulating sea ice thickness.
SIPW01 13th September 2017
11:00 to 11:45
Dirk Notz When is all the sea ice gone?
Co-author: Julienne Stroeve (University College London)

We examine the future evolution of Arctic sea ice, focusing in particular on the allowable carbon dioxide emissions that would prevent sea-ice loss in the various seasons. In this context, the relationship between model simulations and observations is crucial, and we will briefly discuss why it is so difficult to identify models that most reliably simulate the future of Arctic sea ice. Based on this discussion, we will then introduce an observation-based estimate of the future evolution of Arctic sea ice that considers our physical understanding of the main processes that cause the ongoing ice loss.
SIPW01 13th September 2017
11:45 to 12:30
Pat Langhorne Changes to sea ice thickness distribution due to Ice Shelf Water
Co-authors: Inga Smith, Greg Leonard, Andrew Pauling, Pat Wongpan, David Dempsey, Ken Hughes, Craig Purdie, Eamon Frazer (University of Otago), Mike Williams, Natalie Robinson, Craig Stevens (NIWA), Alena Malyarenko, Stefan Jendersie (NIWA & University of Otago), Wolfgang Rack, Gemma Brett, Dan Price (University of Canterbury), Christian Haas (Alfred Wegener Institute), Cecilia Bitz (University of Washington), Andy Mahoney (Geophysical Institute) and Tim Haskell (Callaghan Innovation Ltd)

Satellite observations show that the winter maximum sea ice extent around Antarctica has been increasing slowly over the past three decades, a behaviour superficially at odds with “global warming”.  One hypothesis is that an increase in freshwater input from the base of ice shelves has influenced sea ice extent. This process can drive seawater temperatures below the surface freezing point. Ice crystals then persist in the supercooled water and add to the mass of the coastal sea ice cover. The crystals may form a porous, friable layer, called the sub-ice platelet layer, which can be several metres thick beneath the two-metres of sea ice. Consequently platelet ice formation not only causes sea ice to be thicker, but it also alters the hydrostatic relationship between sea ice elevation and thickness, influencing satellite altimeter determination of sea ice thickness.

Here we describe ice shelf–sea ice interaction at a range of scales from parameterization in an Earth System Model, to the sub-metre detail of winter ice-ocean relationships. On a regional scale we have focused on a location affected by an ISW outflow at the surface. Regional ocean modeling and satellite altimeter observations provide context for airborne sea ice thickness surveys using electromagnetic (EM) induction sounding. These regional surveys have been supported over smaller geographic areas by detailed on-ice sea ice and snow thickness measurements, by on-ice EM induction transects of sea ice thickness, and by under-ice oceanographic observations that track the heat deficit and mixing in the upper ocean at selected sites.

SIPW01 14th September 2017
09:00 to 09:45
Andrew Wells Models of multi-scale and multi-phase sea ice thermodynamics
Sea ice is a multi-phase material, consisting of a mixture of solid ice crystals and liquid brine. The properties of this mixture vary significantly during initial ice growth, from the growth of suspensions of frazil ice crystals in supercooled leads and polynyas through to a reactive porous material during consolidated congelation growth. The resulting mixture is also inherently multi-scale, with the macroscopic scales of interest such as ice depth or mixed layer depth being many order of magnitude larger than the scale of an individual ice crystal. This talk will provide an introduction to key continuum models of the multi-phase and multi-scale thermodynamics of sea ice growth. I will introduce so-called "mushy layer theory" for characterising the evolution of reactive porous sea ice, and also review theories of crystal suspension dynamics derived from a master equation. Selected case studies will be used to illustrate the application of these theories to predict ice accumulation rates, structural properties of ice, and interaction with convective flow.
SIPW01 14th September 2017
09:45 to 10:30
Daniela Flocco Modeling Arctic melt ponds
SIPW01 14th September 2017
11:00 to 11:45
Robert Bridges Sea ice research - needs and gaps
SIPW01 14th September 2017
11:45 to 12:30
Erik Almkvist Different ice observation methods in marine operations
SIPW01 14th September 2017
14:00 to 14:30
Predrag Popovic Simple rules govern the patterns of Arctic sea ice melt ponds
Co-authors: BB Cael (MIT), Mary Silber (University of Chicago), Dorian Abbot (University of Chicago)

Climate change, amplified in the far north, has led to a rapid sea ice decline in recent years. Melt ponds that form on the surface of Arctic sea ice in the summer significantly lower the ice albedo, thereby accelerating ice melt. Pond geometry controls the details of this crucial feedback. However, a question of modeling pond geometry remains unresolved. Here we show that an extremely simple model of voids surrounding randomly sized and placed overlapping circles reproduces the essential features of pond patterns. The model has only two parameters, circle scale and the fraction of the surface covered by voids, which we choose by comparing the model to pond images. Using these parameters the void model robustly reproduces all of the examined pond features such as the ponds' area-perimeter relationship and the area-abundance relationship over nearly 7 orders of magnitude. By analyzing airborne photographs of sea ice, we also find that the pond width distribution is surpris ingly constant across different years, regions, and ice types. These results demonstrate that the geometric and abundance patterns of Arctic melt ponds can be simply described, and can guide future models of Arctic melt ponds to improve predictions of how sea ice will respond to Arctic warming.
SIPW01 14th September 2017
14:30 to 15:00
Yiping Ma Ising model for melt ponds on Arctic sea ice
Perhaps the most iconic feature of melting Arctic sea ice is the formation of distinctive, complex ponds on its surface during late spring. The evolution of melt ponds and their geometrical characteristics determines the albedo of sea ice, a key parameter in climate modeling. However, a theoretical understanding of this evolution, and predictions of geometrical features, have remained elusive. To address this fundamental problem in polar climate science, here we introduce a two dimensional random field Ising model for melt ponds. The ponds are identified as metastable states of the system, where the binary spin variable corresponds to the presence of melt water or ice on the sea ice surface. With only a minimal set of physical parameters, the model predictions agree very closely with observed power law scaling of the pond size distribution and critical length scale where melt ponds undergo a transition in fractal geometry.

This is joint work with
Ivan Sudakov, Courtenay Strong, and Kenneth M. Golden.
SIPW01 14th September 2017
15:30 to 16:00
Woosok Moon Nonlinear stochastic time series analysis for sea ice and climate
SIPW01 14th September 2017
16:00 to 17:00
Grae Worster Brine rejection from sea ice
Brine rejection from sea ice provides a significant contribution to the buoyancy flux that drives ocean circulations.  Indeed, it provides the dominant contribution in the case of polynyas but the situation with consolidated sea ice is more complex.  Although salt is rejected completely by the ice crystals that form when the ocean freezes, it can be retained as saturated brine within the interstices of sea ice.  Buoyancy-driven convection driven in the interior of sea ice can cause the dense brine to drain into the underlying ocean via brine channels that form by dissolution of the ice matrix.  These intricate interactions between fluid flow and phase change occur on the scale of millimetres to centimetres within sea ice but their consequences must be captured within the sea-ice components of climate models.  I will describe the fundamental physical processes that govern the occurrence and rates of brine rejection from sea ice, and show how the understanding gained from detailed mathematical models of local, three-dimensional processes can be incorporated into an appropriately parameterised one-dimensional model of convection in sea ice suitable for inclusion in climate models.
SIPW01 15th September 2017
08:55 to 09:00
Opening remarks, Danny Feltham
SIPW01 15th September 2017
09:00 to 09:40
Bruno Tremblay Using sea-ice deformation fields to constrain the mechanical strength parameters of geophysical sea ice
Co-author: Amelie Bouchat (McGill UniversityUsing sea-ice deformation fields to constrain the 2 mechanical strength parameters of geophysical sea ice)

We investigate the ability of viscous-plastic (VP) sea-ice models with an elliptical yield curve and normal flow rule to reproduce the shear and divergence distributions derived from the RADARSAT Geophysical Processor System (RGPS). In particular, we reformulate the VP elliptical rheology to allow independent changes in the ice compressive, shear and isotropic tensile strength parameters (P*, S*, T* respectively) in order to study the sensitivity of the deformation distributions to changes in the ice mechanical strength parameters. Our 10-km VP simulation with standard ice mechanical strength parameters P∗= 27.5 kNm−2 , S∗ = 6.9 kNm−2, and T∗ = 0 kNm−2 (ellipse aspect ratio of e = 2) does not reproduce the large shear and divergence deformations observed in the RGPS deformation fields, and specifically lacks well-defined, active linear kinematic features (LKFs). Probability density functions (PDFs) for the shear and divergence of are nonetheless not Gaussian. Simulations with a reduced compressive or increased shear strength are in good agreement with RGPS-derived shear and divergence PDFs, with relatively more large deformations compared to small deformations. The isotropic tensile strength of sea ice on the other hand does not significantly affect the shear and divergence distributions. When considering additional metrics such as the ice drift error, mean ice thickness fields, and spatial scaling of the deformations, our results suggest that reducing the ice compressive strength is a better solution than increasing the shear strength when performing Arctic-wide simulations of the sea-ice cover with the VP elliptical rheology.
SIPW01 15th September 2017
09:40 to 10:00
David Rees Jones Frazil-ice dynamics in mixed layers and sub-ice-shelf plumes
The growth of frazil ice is an important mode of ice formation in the cryosphere. We consider models of a population of ice crystals with different sizes to provide insight into the treatment of frazil ice in large-scale models. We apply our model to a simple mixed layer (such as at the surface of the ocean) and to a buoyant plume under a floating ice shelf. We provide numerical calculations and scaling arguments to predict the occurrence of frazil-ice explosions (periods of rapid ice growth). Faster crystal growth rate, higher secondary nucleation and slower gravitational removal make frazil-ice explosions more likely. We identify steady-state crystal size distributions, which are largely insensitive to crystal growth rate but are affected by the relative importance of secondary nucleation to gravitational removal. Finally, we show that the fate of plumes underneath ice shelves is dramatically affected by frazil-ice dynamics. Differences in the parameterization of crystal growth and nucleation give rise to radically different predictions of basal accretion and plume dynamics; and can even impact whether a plume reaches the end of the ice shelf or intrudes at depth.

Further details can be found at www.the-cryosphere-discuss.net/tc-2017-155/ (Rees Jones, D. W. and Wells, A. J.).

SIPW01 15th September 2017
10:00 to 10:20
Harold Heorton Relationship between sea ice deformation and rheology
The drift and deformation of sea ice floating on the polar oceans is caused by the applied wind and ocean currents. The deformations of sea ice over ocean basin length scales have observable patterns. Cracks and leads can be observed in satellite images and within the velocity fields generated from floe tracking. In a climate sea ice model the deformation of sea ice over ocean basin length scales is modelled using a rheology that represents the relationship between stresses and deformation within the sea ice cover. Here we investigate the link between emergent deformation characteristics and the underlying internal sea ice stresses and force balance using the Los Alamos numerical sea ice climate model.

In order focus on the role of sea ice rheologies in producing deformation we have developed an idealised square domain that tests the model response at spatial resolutions of up to 500 m. We use the Elastic Anisotropic Plastic and Elastic Viscous Plastic rheologies, comparing their stability over varying resolutions and time scales. Sea ice within the domain is forced by idealised winds in order to compare the confinement of wind stresses and internal sea ice stresses. We document the characteristic deformation patterns of convergent, divergent and rotating stress states.
SIPW01 15th September 2017
10:20 to 10:40
Stefanie Rynders Impact of surface wave mixing on sea ice and mixed layer depth
Co-authors: Yevgeny Aksenov (National Oceanography Centre), Daniel Feltham (University of Reading), George Nurser (National Oceanography Centre), Gurvan Madec (L’OCEAN Sorbonne Universités)

Breaking waves cause mixing of the upper water column and present mixing schemes in ocean models take this into account through surface roughness. Sea surface roughness can be calculated from significant wave height, which is commonly parameterised from wind speed. We present results from simulations using modelled significant wave height instead, which accounts for the presence of sea ice and the effect of swell. The simulations use the NEMO ocean model coupled to the CICE sea ice model in a one degree configuration, with wave information from the ECWAM model of the European Centre for Medium-Range Weather Forecasts (ECMWF). It is found that in the simulations with modelled wave height mixing is reduced under the ice cover, since the parameterisation from wind speed overestimates wave height in the ice-covered regions. Decreased mixing decreases vertical heat fluxes to and from the sea ice, which in turn affects sea ice concentration and ice thickness. In the Arctic, ice thicknesses increase overall, with higher increases in the Western Arctic and decreases along the Siberian coast. In the Southern Ocean the meridional gradient in ice thickness and concentration is increased. The new mixing parameterisation improves sea ice volumes in the simulation, especially in the Southern Ocean, where the model has difficulty reproducing the winter sea ice volumes. The mixed layer depth under sea ice is also improved, without affecting mixed layer depth in ice-free regions. Wave and sea ice coupling will become more important in the future, when wave heights in a large part of the Arctic are expected to increase due to sea ice retreat and a larger wave fetch. Therefore, wave mixing constitutes a possible positive feedback mechanism for sea ice decline. The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 607476.
SIPW01 15th September 2017
11:10 to 11:30
Yevgeny Aksenov Waves, ice and ocean in the future projections of the Arctic and Southern oceans
Co-authors: Lucia Hosekova (University of Reading, UK), Stefanie Rynders (National Oceanography Centre, UK), Danny Feltham (University of Reading, UK), Gurvan Madec (Institut Pierre Simon Laplace (IPSL), France), George Nurser (National Oceanography Centre, UK), Tim Williams (Nansen Environmental and Remote Sensing Center (NERSC), Norway), Andrew Coward (National Oceanography Centre, UK)

We present a new development to couple a Sea Ice-Ocean General Circulation Model (OGCM) with ocean waves and analyse the impact of the waves on sea ice and upper ocean. The motivation for the study stems from the recent changes in the Arctic sea ice: not only sea ice extent has been significantly lower in the recent decade than the climatology in summer and winter, but also it is much more broken and mobile, allowing the ocean surface waves propagate in the central Arctic. This mobile sea ice moderates momentum transfer from the atmosphere to the ocean and affects the heat storage in the mixed layer and halocline. We present the simulations with the newly implemented sea ice rheology, combined with floe size distribution analysis and discuss the implications of the observed wave increase and sea ice fragmentation for the present and future of the Polar Oceans. The study was a part of the EU FP7 Project ‘Ships and waves reaching Polar Regions (SWARP)’ and is linked to several ongoing UK national research initiatives.
SIPW01 15th September 2017
11:30 to 11:50
Phil Hwang Winter-to-summer transition of Arctic sea ice breakup and floe size distribution in the Beaufort Sea
Breakup of the near-continuous winter sea ice into discrete summer ice floes is an important transition that dictates the evolution and fate of the marginal ice zone (MIZ) of the Arctic Ocean.  During the spring of 2014, more than 50 autonomous drifting buoys were deployed in four separate clusters on the sea ice in the Beaufort Sea, as part of the Office of Naval Research MIZ program. These systems measured the ocean-ice-atmosphere properties at their location whilst the sea ice parameters in the surrounding area of these buoy clusters were continuously monitored by satellite TerraSAR-X Synthetic Aperture Radar. This approach provided a unique Lagrangian view of the winter-to-summer transition of sea ice breakup and floe size distribution at each cluster between March and August. The results show the critical timings of a) temporary breakup of winter sea ice coinciding with strong wind events and b) spring breakup (during surface melt, melt ponding and drainage) leading to distinctive summer ice floes. Importantly our results suggest that summer sea ice floe distribution is potentially affected by the state of winter sea ice, including the composition and fracturing (caused by deformation events) of winter sea ice, and that substantial mid-summer breakup of sea ice floes is likely linked to the timing of thermodynamic melt of sea ice in the area. As the rate of deformation and thermodynamic melt of sea ice has been increasing in the MIZ in the Beaufort Sea, our results suggest that these elevated factors would promote faster and more enhanced breakup of sea ice, leading to a higher melt rate of sea ice and thus a more rapid advance of the summer MIZ.
SIPW01 15th September 2017
11:50 to 12:10
Ann Keen Investigating future changes in the volume budget of the Arctic sea ice in a coupled climate model
Arctic September sea ice cover has declined at a rate of 13% per decade since satellite observations began, and there is much interest in how this decline will continue in the future, both in terms of the predictability of ice cover in a given year, and in terms of the manner and timing of the transition to a seasonally ice-free Arctic. Global coupled models are arguably the best tool we have for making future projections of the Arctic sea ice, but generate a wide spread of projections of future ice decline. There are many factors potentially contributing to this spread, and it is becoming increasingly clear that as well as investigating ‘integrated’ quantities like ice cover and volume directly, it is also necessary to consider, compare and evaluate the underlying processes, and how they change.

Here we consider the volume budget of the sea ice in the Arctic Basin in the HadGEM2-ES global coupled model (which was the UK/Met Office contribution to CMIP5), and how the budget components evolve during the 21st century under a range of different forcing scenarios. In terms of what happens per unit surface area of the ice, the processes that change most as the climate warms are summer melting at the top surface of the ice, and basal melting due to extra heat from the warming ocean. However, due to the declining ice cover these are not the budget components that contribute most to reductions in the ice volume, and the largest budget change is a reduction in the total amount of basal ice formation during the autumn and early winter.

The choice of forcing scenario affects the rate of ice decline and the timing of change in the volume budget components, but for this model and for the range of scenarios considered for CMIP5, the mean changes in the volume budget depend on the evolving ice area, and are independent of the speed at which the ice cover declines.
SIPW01 15th September 2017
12:10 to 12:30
Jamie Rae How much should we believe correlations between Arctic cyclones and sea ice extent?
I will present an analysis of Arctic summer cyclones in a climate model and in a reanalysis dataset, including results from a cyclone identification and tracking algorithm, and correlations between characteristics of the cyclones and September Arctic sea ice extent.  Results will be presented for output from model simulations at two resolutions, and for the reanalysis, using two different tracking variables (mean sea-level pressure and 850 hPa vorticity) for identification of the cyclones.  I will explore the influence of the tracking variable, the spatial resolution of the model, and spatial and temporal sampling, on the correlations.  I will conclude that the correlations obtained depend on all of these factors, and that care should be taken when interpreting the results of such analyses, especially when the focus is on one reanalysis, or output from one model, analysed with a single tracking variable for a short time period.
SIPW01 15th September 2017
13:30 to 14:10
Julienne Stroeve Integrating Observations and Models to Better Understand a Changing Arctic Sea Ice Cover
SIPW01 15th September 2017
14:10 to 14:30
Ian Renfrew Atmospheric response to marginal-ice-zone drag parameterisation
A physically-based parameterization of atmospheric surface drag over the marginal-ice-zone has recently been validated and tuned based on a large set of observations of surface stress from the ACCACIA project (Elvidge et al. 2016, Atmos. Chem. and Physics). This parameterization has now been implemented in the Met Office Unified Model (MetUM) and is available for both weather and climate applications. Here we present test results for a case study of a cold-air outbreak over and downstream of the MIZ, and for a collection of cases from the ACCACIA field campaign. Our focus is on the response of the atmosphere to the changes in surface drag. Preliminary results show that the new parameterization has a significant impact on simulated boundary layer conditions. For example, boundary layer temperatures over the MIZ during cold air outbreaks are generally reduced by 2-3 K in the model, in response to markedly reduced surface heat fluxes. Comparisons with aircraft observations reveal the changes to generally be beneficial. The implications of these changes for the climate system will be discussed.
SIPW01 15th September 2017
14:30 to 14:50
Michel Tsamados Challenges in estimating ocean surface stresses in sea ice covered Arctic and Antarctic regions
SIPW01 15th September 2017
14:50 to 15:30
Peter Wadhams Statistics of the sea ice thickness distribution
Measurements of the shape of the sea ice underside by submarine and other methods have enabled us to determine the statistical distributions which described under-ice morphology. Two of the most interesting findings are that (a) the probability density function of deep ice draft
and of the drafts of individual pressure ridges both obey a negative exponential distribution, and (b) the distribution of the spacings between successive pressure ridge keels obey a log-normal distribution. Agreement with the equations is very close. Other parameters of the ice underside, including fractal properties, are much more variable, as are characteristics such as the slop angles of pressure ridges. We examine to what extent the topography of the upper ice surface (freeboard instead of draft; sails instead of keels) obeys the same relationships, and speculate on the physical reasons for these distributions.
SIPW01 15th September 2017
16:00 to 16:20
Christian Haas Arctic Sea Ice Thickness Change
SIPW01 15th September 2017
16:20 to 16:40
Alex West Using Arctic ice mass balance buoys for model evaluation
Since 1993 the Arctic Ocean has seen the deployment of over 100 ice mass balance buoys (IMBs), devices which measure elevation of the sea ice surface and base, as well as internal ice temperatures at a vertical resolution of 10cm.  Here the thermodynamic data provided by the IMBs is used to evaluate the sea ice simulation of the CMIP5 model HadGEM2-ES, which simulates anomalously high summer melting and winter freezing in the recent historical period.  Monthly mean fluxes of topmelt, snowfall, conduction, basal growth and ocean-to-ice heat are calculated for the entire IMB network, giving a distribution of around 500 data points for each variable. Model evaluation is concentrated in two regions of the Arctic that are particularly densely sampled by the IMBs, the North Pole and the Beaufort Sea. Distributions of modelled and observed fluxes in these regions are compared, and severe biases in June top melting fluxes and winter conductive fluxes are identified which are too large to be attributed to sampling biases in the IMBs.  Consistent with previously identified biases in the Arctic climate simulation of HadGEM2-ES, the results allow detailed attribution of the sea ice simulation biases to particular drivers in the atmosphere and sea ice.
SIPW01 15th September 2017
16:40 to 17:00
Ed Blockley Impact of initialising sea ice forecasts using CryoSat-2 thickness observations for seasonal sea ice prediction with the Met Office GloSea system
Met Office seasonal predictions are made with the GloSea coupled forecasting system. The (NEMO) ocean and (CICE) sea ice components of GloSea are initialised using analysis fields from the FOAM ocean-sea ice analysis and forecast system. FOAM assimilates satellite and in-situ observations of temperature, salinity, sea level anomaly and sea ice concentration each day using the NEMOVAR 3D-Var scheme. Sea ice thickness is not yet assimilated by FOAM but the Met Office are currently developing capability to assimilate sea ice freeboard and thickness observations from CryoSat-2 and SMOS sensors within the NEMOVAR 3D-Var framework.

Here we present the findings of a recent study undertaken to assess the impact on the evolution of sea ice seasonal forecasts of initialising with CryoSat2-derived thickness observations. We will show that the initialisation of thickness leads to improved skill for seasonal predictions of Arctic summer sea ice extent and ice-edge location whilst highlighting persistent biases in the modelled thickness distribution.
SIPW01 15th September 2017
17:00 to 17:20
David Schroeder New insight from CryoSat-2 sea ice thickness for sea ice modelling
Estimates of Arctic sea ice thickness are available from the CryoSat-2 radar altimetry mission during the ice growth seasons since 2010. We derive the sub-grid scale ice thickness distribution (ITD) with respect to 5 ice thickness categories used e.g. in the sea ice component CICE of HadGEM3 climate simulations: (1) ice thickness h 3.6 m. This allows us both to verify the simulated cycle of ice thickness and to initialize the ITD in stand-alone simulations with the sea ice model CICE. We find that a default CICE simulation strongly underestimates the ice thickness, in spite of doing a reasonable job regarding the inter-annual variability of summer sea ice extent. We can identity the underestimation of winter ice growth being responsible and show that using ice and snow conductivity values on the upper end of the observed range (2.63 and 0.5 W/m/K) makes sea ice growth more realistic and generally improves the model simulation. Sensitivity studies provide insight on the role of ice strength, momentum and heat turbulent fluxes on the annual cycle of sea ice thickness. We show that the width of ITD plays an important role for the summer lead fraction and basal ice melt. Furthermore, a major discrepancy is revealed regarding the annual cycle of sub-grid scale thick sea ice (category 5). According to Cryosat-2 there is a strong formation of thick ice during winter, but hardly any thick ice survives the summer. CICE simulations only show a weak seasonal cycle, indicating that both the formation and the melting of thick is underestimated. Coupled simulations with the ocean – sea ice model NEMO-CICE confirm our results highlighting that sea ice physics and parameters are responsible for differences with Cryosat estimates and improvements are required.
SIP 19th September 2017
15:00 to 16:30
Luke Bennetts Wave-induced collisions of thin floating disks
Collisions between two thin floating disks forced by regular water waves are studied for a range of wave amplitudes and lengths, using laboratory wave basin experiments and a mathematical model. Three collision regimes are identified from the experiments in terms of collision frequency and strength, and the collisions are shown to be caused by drift for short incident wavelengths and relative surge motion between the disks for longer incident waves. The model is based on slope-sliding theory for the wave-induced disk motions, and rigid-body collisions. It is shown to predict collision frequencies and velocities accurately for long incident wavelengths. Incorporating drift and wave scattering forces into the model is shown to capture the collision behaviours for short incident wavelengths.

OFBW35 25th September 2017
09:30 to 09:40
Jane Leeks, David Abrahams Welcome & Introduction
OFBW35 25th September 2017
09:40 to 10:00
Daniel Feltham Introduction to Sea Ice Climate Models
OFBW35 25th September 2017
10:00 to 10:40
Dirk Notz What do Climate Models need Sea Ice for?
OFBW35 25th September 2017
10:40 to 11:20
Questions and Discussion
OFBW35 25th September 2017
11:40 to 12:20
Cecilia Bitz What Sea Ice Physics is Missing from Models?
OFBW35 25th September 2017
12:20 to 13:00
Questions and Discussion
OFBW35 25th September 2017
13:00 to 14:30
Lunch and Posters
OFBW35 25th September 2017
14:30 to 15:10
Elizabeth Hunke Modelling Approaches to Address Sea Ice Complexity
OFBW35 25th September 2017
15:10 to 15:50
Questions and Discussion
OFBW35 25th September 2017
16:10 to 16:50
Daniel Feltham Panel Discussion and Wrap-Up
SIP 26th September 2017
15:00 to 16:30
Nico Gray Recent advances in granular rheology and possible applications to large scale sea ice dynamics
SIP 29th September 2017
14:00 to 16:00
Eugen Varvaruca Bifurcation theory in the context of nonlinear steady water waves
Global bifurcation theory is the most successful method for proving existence of fully nonlinear steady water waves of large amplitude. I will present an overview of some of the most significant results in abstract bifurcation theory (the Crandall--Rabinowitz local bifurcation theorem, the global topological theories of Rabinowitz and of Kielhofer, and the global real-analytic theory of Dancer, Buffoni and Toland), together with some aspects concerning the application of these results in the context of various types of steady nonlinear water waves (gravity waves, capillary-gravity waves, and waves beneath an elastic ice sheet).
SIPW02 2nd October 2017
09:45 to 10:30
Hung Tao Shen River Ice – Process, Theory, and Mathematical Modeling
River ice research has largely been driven by engineering and environmental problems that concern society. These concerns have been on ice jam flooding, hydropower operation, inland navigation, winter time ecology, and the influence of ice on water quality. River ice phenomena include formation, evolution, transport, accumulation, deterioration, and dissipation of various forms of ice. These phenomena involve complex interactions between hydrodynamic, mechanical, and thermal processes, under the influence of meteorological and hydrological conditions as well as the operations of water resources engineering projects. Most of the river ice phenomena also occur in sea ice, except that river ice forms in freshwater confined within channels. Mathematical modeling of river ice processes faces similar problems as sea ice, but in much smaller spatial and time scales because of the strong boundary effects. There has been only a relatively small group of researchers engaged in this no n-traditional topic of river hydraulics. However, important advances have been made in the last couple of decades. In this presentation, river ice processes and major research advances enabled by mathematical modeling will be discussed. These will include frazil and anchor formation, surface ice transport and ice jam dynamics, undercover frazil jam/hanging dam evolution, breakup processes, and sediment transport with ice effects.

Keywords: River ice, freeze up, frazil ice, ice jams, breakup, hydrodynamics, mathematical modeling
SIPW02 2nd October 2017
11:00 to 11:45
Mike Meylan Mathematical Challenges in Modelling Wave Scattering in the Marginal Ice Zone
When I started modelling wave scattering by sea ice in 1991, even the simplest two-dimensional model of wave scattering by a single ice floe had not been solved accurately. By 1996 I had developed three-dimensional models for an ice floe and a paradigm for the inclusion of scattering in wave prediction code. Some of this work was done during a month I spent at the Scott Polar Research Institute in Cambridge in 1995.Looking back, and returning to Cambridge 22 years later, it is striking (and slightly depressing) how progress on this topic has stalled. The reasons for this are largely mathematical and in this talk I will try and give a flavour of these difficulties and suggest some possible methods to tackle them.
SIPW02 2nd October 2017
11:45 to 12:30
Stefanie Rynders Modelling dynamics of the marginal ice zone, including combined collisional and EVP rheology
Co-authors: Yevgeny Aksenov (National Oceanography Centre), Daniel Feltham (Centre for Polar Observations and Modeling, University of Reading), George Nurser (National Oceanography Centre)

Exposure of large, previously ice-covered areas of the Arctic Ocean to the wind and surface ocean waves results in the Arctic pack ice cover becoming more fragmented and mobile, with large regions of ice cover evolving into the Marginal Ice Zone (MIZ). The need for better climate predictions, along with growing economic activity in the Polar Oceans, necessitates climate and forecasting models that can simulate fragmented sea ice with greater fidelity. The main focus here is on sea ice rheology. A Combined Collisional, reflecting the granular behaviour of MIZ sea ice, and Elastic-Viscous-Plastic (EVP) rheology is implemented in an idealised and a global sea ice-ocean model. The effect of surface waves on ice motion is included in the turbulent kinetic energy or ‘granular temperature’ of ice floes. The granular temperature is validated with accelerometer data. It is found that the combined rheology has impact beyond the marginal ice zone, influencing ice motion and sea ice thickness. Taking into account the fragmented nature of MIZ ice also allows for another dynamical feature of the MIZ: in idealised channel model simulations ice edge jets occur when variable floe size is used. The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 607476.
SIPW02 2nd October 2017
13:30 to 14:15
Vernon Squire A different perspective on wave-ice interaction research
The focus of this talk will be on the two research strands that currently exemplify wave-ice interaction research, namely: (i) the continuum paradigm, which leads naturally into parametrizations that can potentially be incorporated straightforwardly into wave forecasting models such as WAVEWATCH III or global climate models; and (ii) methodology that endeavours to represent the physics of each constituent process as faithfully as possible, acknowledging from the outset that approximations are inevitable. The advantages and disadvantages of each approach will be discussed, especially in the context of implications for the design of field experiments and the subsequent analysis of any data collected. It is asserted that field experiments grounded in the continuum paradigm are particularly challenging because the number of degrees of freedom in Nature is huge compared with a typical model. The consequences of using a linear ansatz will also be made clear, recognizing that very nearly all current mathematical models of the phenomenon are linear yet the few data that are available suggest that the assumption of linearity is inconsistent with observation in some cases and presupposes outcomes that are too restrictive.
SIPW02 2nd October 2017
14:15 to 15:00
John Grue Dead water effect on drift of icebergs
Observations/measurements of the drift of an iceberg in Antarctica are motivation of the lecture. Particularly two measurements of the internal waves generated by the iceberg are discussed. These measurements are connected to Fridtjof Nansen's historical observations of the dead water on FRAM, published in Nansen (1897). The dead water resistance on FRAM is first obtained empirically from Nansen's observations. A strongly nonlinear interfacial model of the dead water resistance is then outlined with calculations relevant to the FRAM ship. The intersection of the resistance curves obtained empirically and theoretically determines accurately the speed of FRAM. This intersection becomes a function of the level of the pycnocline. The nonlinear and linear dead water wakes are then obtained at the low subcritical speeds. The connection between the dead water effect on FRAM and the ice berg case are discussed. The considerable increase in the dead water resistance at small subcritical speed, which FRAM did not overcome, is discussed. The same resistance slope seems to limit the speed of the iceberg drift where the observed internal wave Froude number is subcritical at a value of 0.6. References: J. Grue (2015). Nonlinear dead water resistance at subcritical speed. Phys. Fluids 27, 08213. J. Grue (2017). Calculating FRAM's dead water. In: The Ocean in Motion - Circulation, waves polar oceanography. Springer-Verlag, Oceanography Series. Eds. M.G. Velarde, R. Yu. Tarakanov, A.V. Marchenko. 70th Anniversary of Eugene G. Morozov. J. Morison and D. Goldberg (2012). A brief study of the force balance between a small iceberg, the ocean, sea ice, and atmosphere in the Weddell Sea. Cold regions science and technology, 76-77, 69-76.
SIPW02 2nd October 2017
15:30 to 16:15
Elizabeth Hunke Where ice is not: The liquid phase in the sea ice model CICE
Viewed at a macroscopic scale, the liquid phase of the sea ice pack exhibits a stable, vertical density profile with relatively fresh melt water lying above saltier, denser brine within the ice and much denser seawater below. These layers interact through freezing, melting, dissolution and drainage processes. This talk will overview the representation of these processes in the sea ice model CICE, with indications of which ones may be important for simulating sea ice volume.
SIPW02 2nd October 2017
16:15 to 17:00
Aleksey Marchenko Damping of surface wave in MIZ of the Barents Sea: field observations and modeling
Presentation will include an overview of field measurements of waves performed from drift ice in the Barents Sea since 2006. It includes observations of ice motion during events of wave propagation, measurements of sea current velocities in under ice boundary layer, water pressure at different depths, accelerations and angular velocities of floes. The data are used for the calculation of dispersion properties of observed waves and characteristics of under ice turbulence. The coefficient of wave attenuation is calculated using equation of floe motion along the water surface with relatively common assumptions about floe-floe interactions and known solution describing oscillating boundary layer near the bottom of floating ice. Numerical values of the coefficient are reconstructed using the data of field measurements. The evolution of wave spectra in MIZ of the North-West Barents Sea is compared with the wave spectra calculated from the high resolution satellite image (SAR).
SIPW02 3rd October 2017
09:00 to 09:45
Luke Bennetts Modelling water wave overwash of ice floes
I will summarise progress towards modelling wave overwash of ice floes, which (after breakup) is arguably the most important nonlinear phenomenon in wave–ice interactions, and certainly the most striking one. The phenomenon is unique to wave–ice interactions, occurring because the small freeboards of ice floes allow waves with relatively modest (non-extreme) amplitudes to wash over their upper surfaces when differential motion between the floe and the surrounding wave field exists. Overwash impacts floes thermodynamically, and dissipates wave energy, thus reducing the distances waves penetrate into the ice-covered ocean. From a mathematical modelling perspective, it is a highly nonlinear phenomenon, meaning it cannot be captured by standard perturbation techniques. I will present a bespoke overwash model, along with supporting laboratory experiments and numerical CFD simulations. Applying the methodology to simplified versions of the problem will be shown to provide insights into model performance.

Co-authors: David Skene (Uni Adelaide); Michael Meylan (Uni Newcastle); Alessandro Toffoli (Uni Melbourne); Filippo Nelli (Swinburne Uni Tech); Kevin Maki (Uni Michigan)
SIPW02 3rd October 2017
09:45 to 10:30
Emilian I Parau Nonlinear hydroelastic waves and related flows
A review of some the results concerning nonlinear hdyroelastic waves will be given. We will present waves forced by moving pressures and solitary waves on top of a fluid covered by an ice plate, modelled as a thin elastic plate. The fluid is either of constant density of stratified and two-dimensional or three-dimensional problems are considered.
SIPW02 3rd October 2017
11:00 to 11:45
Olga Trichtchenko Computing Flexural-Gravity Waves
Co-authors: Emilian Parau (University of East Anglia), Jean-Marc Vanden-Broeck (University College London), Paul Milewski (University of Bath)

In this talk we will discuss waves travelling under a layer of ice, which is represented as a thin elastic plate. We will compare and contrast different models for these types of waves and discuss the techniques involved in computing their solutions.
SIPW02 3rd October 2017
11:45 to 12:30
Philippe Guyenne Numerical study of solitary wave attenuation in a fragmented ice sheet
Co-author: Emilian Parau (University of East Anglia)

A numerical model for phase-resolved simulation of nonlinear ocean waves propagating through fragmented sea ice is proposed. This model solves the full time-dependent equations for nonlinear potential flow coupled with a nonlinear thin-plate formulation for the ice cover. The coefficient of flexural rigidity is allowed to vary spatially so that distributions of ice floes can be directly specified in the physical domain. Two-dimensional simulations are performed to examine the attenuation of solitary waves by scattering through an irregular array of ice floes.
SIPW02 3rd October 2017
13:30 to 14:15
Pat Langhorne In situ detection of fluid movement in Antarctic land-fast sea ice
Co-authors: Pat Wongpan (University of Otago), Ken Hughes (University of Otago & University of Victoria), Inga J, Smith (University of Otago)

Vertical temperature strings are used in sea ice research to study heat flow, ice growth  rate, and ocean-ice-atmosphere interaction. We demonstrate the feasibility of using temperature fluctuations as a proxy for fluid movement, a key process to resupply nutrients to  Antarctic land-fast sea ice algal communities. Four thermistor arrays (including two mid-winter records) were deployed in the land-fast sea ice of McMurdo Sound, Antarctica. By  smoothing temperature data with the robust LOESS method, we obtain temperature fluctuations that cannot be explained by insolation or heat loss to the atmosphere. Statistical  distributions of these temperature fluctuations are investigated with sensitivities to the distance from the ice-ocean interface, average ice temperature, and sea ice structure. Temperature fluctu ations are discrete events that have greatest magnitude close to the ice-ocean interface ( −3 x25E6;C. At temperatures > −3 ◦C fluctuations occur for 43% of the time, when the ice is colder (−3 to −5 ◦C) this active period is reduced to 11%. Assuming temperature fluctuations occur at a critical Rayleigh number derived from mushy layer theory, we parameterise a measure of permeability of this thick (>1 m)  Antarctic land-fast sea ice in terms of average ice temperature.  This permeability decreases by three orders of magnitude between the ice-ocean interface  and ∼70 mm above it, as the sea ice temperature changes from the freezing point to −5 ◦C.   The same permeability parameterisation is independent of whether the sea ice has a columnar crystal structure or has a more disordered platelet ice structure, characteristic of proximity to an ice shelf.
SIPW02 3rd October 2017
14:15 to 15:00
Hayley Shen Wave Propagation in Viscoelastic Materials over Water
Ice covers over water modify the mass, energy, and momentum transfer between the atmosphere and ocean. Ocean wave propagation is one of the numerous topics from these three basic processes. Because of the Arctic ice reduction, longer fetch has increased both the intensity and the dominant wave period. Longer period waves damp much less. They thus propagate further into ice covers. The contemporary Arctic system cannot be properly evaluated without a good grasp of the growing presence of waves under ice covers. Ice covers are complex materials. Even a continuous solid ice cover does not fit into a simple constitutive model. In the field ice covers often are consisted of discontinuous pieces of various sizes and shapes, mixed with open water or slurry of ice crystals. Such a composite cover has been idealized as a linear viscoelastic material. This hypothesis is based on a simple physical argument: all materials under deformation simultaneously store some and dissipate some energy. The first order approximation is therefore a linear viscoelastic model. To test this hypothesis, the dominant characteristics of the model must be thoroughly understood. The most important characteristic of wave propagation is the dispersion relation. Even with a simple linear viscoelastic model, the dispersion relation is complicated. There are many roots all satisfy the dispersion relation. All of them may be present under different conditions. In this talk, a description of these roots and their physical meanings will be presented. Their presence has been found in other fields. Knowledge from other fields may shed light on how these different wave modes interact under different situations.
SIPW02 3rd October 2017
15:30 to 16:15
Jean-Marc Vanden-Broeck Asymmetric nonlinear flexural waves
Nonlinear waves travelling under an elastic sheet are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. The sheet is modelled by using the theory of Plotnikov and Toland. The problem is solved by boundary integral equation methods and series truncation approaches. Periodic waves, solitary waves and generalised solitary waves are considered. Special attention is devoted to asymmetric waves. Time dependent solutions are also presented.
SIPW02 3rd October 2017
16:15 to 17:00
Andrej Il’ichev Wave patterns beneath an ice cover
We prove existence of the soliton-like solutions of the full system of equations which describe wave propagation in the fluid of a finite depth under an ice cover. These solutions correspond to solitary waves of various nature propagating along the water-ice interface. We consider the plane-parallel movement in a layer of the perfect fluid of the finite depth which characteristics obey the full 2D Euler system of equations. The ice cover is modeled by the elastic Kirchgoff-Love plate and it has a considerable thickness so that the plate inertia is taken into consideration when the model is formulated. The Euler equations contain the additional pressure arising from the presence of the elastic plate freely floating on the liquid surface. The mentioned families of the solitary waves are parameterized by a speed of the wave and their existence is proved for the speeds lying in some neighborhood of its critical value corresponding to the quiescent state. S olitary waves, in their turn, bifurcate from the quiescent state and lie in some neighborhood of it. By other words, existence of solitary waves of sufficiently small amplitudes on the water-ice interface is proved. The proof is conducted with the help of the projection of the required system to the central manifold and further analysis of the resulting reduced finite dimensional dynamical system on the central manifold.
SIPW02 4th October 2017
09:00 to 09:45
Pavel Plotnikov Conformal geometry and hydroelastic waves
SIPW02 4th October 2017
09:45 to 10:30
Mariana Haragus Stability criteria for nonlinear waves in Hamiltonian and reversible systems
We present two general stability/instability criteria for nonlinear waves in Hamiltonian or reversible systems. Both criteria rely upon spectral properties of the linear operators found by linearizing the system at a given wave. We apply these results to some model equations arising in water-wave problems. The focus is on the question of transverse  stability/instability of periodic traveling waves.

SIPW02 4th October 2017
11:00 to 11:45
Timothy Williams A sea ice model with wave-ice interactions on a moving mesh
Timothy Williams, Pierre Rampal, Einar Olason, Syvain Bouillon and Abdoulaye Samake

The neXtSIM (neXt generation Sea Ice Model) sea ice model runs the Maxwell-EB rheology solved with finite element methods on a triangular mesh. It also has thermodynamic effects and a slab ocean included beneath, as well as wave-ice interactions (ice break-up by waves, ice drift due to the wave radiation stress).

An ALE (Arbitrary Lagrangian/Eulerian) scheme has now been implemented in neXtSIM, so that the mesh is usually moving as time goes on. As part of an investigation about the best strategy for coupling the waves-in-ice module (WIM) to neXtSIM, the WIM may now be run on the neXtSIM mesh.

In this talk we give an overview of both neXtSIM and the WIM, and also some results comparing the different coupling strategies for the WIM.
SIPW02 4th October 2017
11:45 to 12:30
Yevgeny Aksenov Impacts of ocean waves on the Polar Sea Ice and Oceans
Co-authors: Lucia Hosekova (University of Reading, UK), Danny Feltham (University of Reading, UK), Tim Williams (Nansen Environmental and Remote Sensing Center (NERSC), Norway), A.J. George Nurser (National Oceanography Centre, UK), Gurvan Madec (Institut Pierre Simon Laplace (IPSL), France), Andrew Coward (National Oceanography Centre, UK)

We examine effects of ocean surface waves on the polar sea ice and ocean using a sea ice-ocean general circulation model NEMO (stands for Nucleus for European Modelling of the Ocean) coupled with the ocean wave model WAM output from model of the European Centre for Medium-Range Weather Forecasts (ECMWF). In the model the wave-ice interactions include: ice fragmentation due to break–up by waves in the vicinity of the ice edge; wave attenuation due to multiple scattering and non-elastic losses in the ice, wave advection and evolution of ice fragmentation. We analyse the impact of the waves on sea ice and the upper ocean, focusing on the marginal ice zone (MIZ) where the wave impacts are the most. The study compares the model results with the observations, and highlights a need to farther theoretical understanding of sea ice fragmentation and summarise requirements for observational techniques. The study was carry out in the EU FP7 Project ‘Ships and waves reaching P olar Regions (SWARP)’.
SIP 4th October 2017
13:30 to 14:30
Gerard Iooss Existence of quasipatterns, solutions of the Bénard-Rayleigh convection
SIPW02 5th October 2017
09:00 to 09:45
Pietro Baldi Time quasi-periodic gravity water waves in finite depth
We consider the water wave equations for a 2D ocean of finite depth under the action of gravity. We present a recent existence and linear stability result for small amplitude standing wave solutions that are periodic in space and quasi-periodic in time. The result holds for values of a normalized depth parameter in a Cantor-like set of asymptotically full measure.
The main difficulties of the problem are the presence of derivatives in the nonlinearity (the system is quasi-linear), and a small divisors problem where the frequencies of the linear part grow in a sublinear way at infinity (like the square root of integers). To overcome these problems we first reduce the linearized operators (which are obtained at each approximate quasi-periodic solution along a Nash-Moser iteration) to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak second Melnikov non-resonance conditions (losing derivatives both in time and space). Such non-resonance conditions are sufficiently weak to be satisfied for most values of the normalized depth parameter, thanks to arguments from degenerate KAM theory.
Joint work with Massimiliano Berti, Emanuele Haus and Riccardo Montalto.
SIPW02 5th October 2017
09:45 to 10:30
Mark Groves Variational existence and stability theory for hydroelastic solitary waves
I will present an existence and stability theory for solitary waves at the interface between a thin ice sheet and an ideal fluid, which is based on minimising the total energy subject to the constraint of fixed total horizontal momentum. The ice sheet is modelled using the Cosserat theory of hyperelastic shells. Since the energy functional is quadratic in the highest derivatives, stronger results are obtained than in the corresponding theory for capillary-gravity water waves. This is joint work with Benedikt Hewer and Erik Wahlén.
SIPW02 5th October 2017
11:00 to 11:45
Thomas Folegot Underwater noise under ice conditions: from the ice chorus to the environmental challenge
Oceans are not silent. And this statement is even more real under ice conditions. The so-called underwater noise chorus is extremely rich and seasonally changing since it is made of multiple components: the natural sound is contributing more than in any other places since ice is a major contributor with sounds of a large diversity according to the type of ice that is present. The biological sounds are also unique in ice conditions since biodiversity in such areas are usually of exceptional nature. At last, the anthropogenic sounds are increasingly contributing to the overall noise chorus, mainly linked with the changing climate conditions that enable human maritime activities to take place. These changing conditions lead to the emerging challenge of underwater noise in ice conditions, especially in the Arctic. Underwater noise is nowadays recognized as being a serious threat for marine life and increasing international regulations are developed in many countries as per the EU Marine Strategy Framework Directive. The merging regulations appeal for new and innovative management and conservation solutions and tools.
SIPW02 5th October 2017
11:45 to 12:30
Tatiana Khabakhpasheva Waves and moving loads along frozen channels
Co-authors: Shishmarev Konstantin (Altay State University, Barnaul, Russia), Korobkin Alexander (University of East Anglia, Norwich, UK)

Hydroelastic waves caused by external loads are well studied for an ice cover of infinite extent. Similar problems, but with an ice cover clamped to the vertical walls in a channel, are studied in less detail. However, the presence of the walls and clamped conditions of the ice to the walls may significantly affect distributions of deflections and stresses in the ice cover. These problems are of practical importance because laboratory experiments on loads moving along an ice cover are performed in ice tanks. The response of the ice cover caused by a moving localized external load is studied numerically and analytically for a channel with rectangular cross section. The equation of viscoelastic thin plate with a given damping coefficient is used for describing oscilations of the ice. The liquid beneath the ice is inviscid and incompressible, the flow is potential. The problem is solved with the help of the Fourier transform along the channel and the method of normal modes across the channel. The numerical results show a significant difference in the distributions of the ice deflections in the channel and in the ice cover of infinite extent for the same loading conditions. For the ice cover of infinite extent there is a single dispersion curve and two critical velocity of hydroelastic wave propagation, whereas the presence of the channel walls leads to the infinite number of the dispersion curves and critical speeds. The critical speeds depend on the channel width and decrease with increase of the distance between the walls of the channel.
SIPW02 5th October 2017
13:30 to 14:15
Stephen Ackley Antarctic Coastal Polynyas: Do Measurements of Winter Processes give clues to modeling Improvements and better model fidelity?
The PIPERS cruise to the Terra Nova Bay (TNB) and Ross Ice Shelf (RIS) polynyas during April-June 2017 focused on joint measurements of air-ice-ocean wave interaction in these polynyas. In Terra Nova Bay, measurements were taken during intense katabatic wind events with sustained winds over 35 meters per second and air temperatures of -15C or below. Despite a relatively short fetch, intense wave fields with wave amplitudes of over 2m and 7-9 sec periods built and large amounts of frazil ice crystals grew. The frazil ice gathered initially into short plumes that eventually were added laterally to create longer, wide streaks. The wave field within the wider streaks was dampened and enhanced the development of pancake ice. Eventually, the open water areas sealed off between the streaks, developing a uniform pancake ice cover of 100 percent concentration. The pancakes continued to grow in diameter and thickness, further attenuating the wave field and the pancake ice growt h then ceased. While the waves died off however, katabatic wind velocities were sustained and resulted in a wide area of concentrated, rafted, pancake ice that was rapidly advected downstream until the end of the katabatic event. The equilibrium thickness of the ice was typically 30 to 40 cm in the pancake ice. High resolution TerraSar-X radar satellite imagery showed the length of the ice area produced in one single event extended over 300km or ten times the length of the open water area during the polynya event. The TNB polynya is therefore an “ice factory” where frazil ice is manufactured into pancake ice floes that are then pushed out of the assembly line and advected, rafted and occasionally piled up into “dragon skin” ice, until the katabatic wind dies off at the coastal source.
SIPW02 5th October 2017
14:15 to 15:00
Alena Malyarenko Interactions between phase change and boundary layer structure
Co-authors: Pat Langhorne (University of Otago), Natalie Robinson (NIWA), Mike Williams (NIWA)

Thermodynamic ice ablation includes both melting and dissolving of the ice. Existing parametrisations are usually based on the 3-equation model, with equations that describe heat and salt flux balances together with the freezing point equation for sea water. However, these equations do not represent both melting and dissolving conditions, or the transition between these conditions. Nor do the 3 equations represent well the two dominant velocity regimes: shear-driven and buoyancy-driven mixing. Turbulent heat and salt transfer coefficients need to reflect the variety of boundary layer structures that can form under different velocity and temperature regimes.

Here the different conditions and velocity regimes are considered in the in context of multi-year observations of temperature, velocity and ablation rate from under the Ross Ice Shelf. These observations of a dissolving ice shelf in sub-zero conditions can be used to constrain transitions from buoyancy-driven mixing to sheer-driven mixing. While these observations are under an ice shelf they are expected to scale to the higher salinities found in sea ice.
SIPW02 5th October 2017
15:30 to 16:15
Jorma Kämäräinen Ship-ice-fluid interaction studies on ice resistance of ships
Ice resistance of a ship can be determined by tests made in full scale, tests made in model scale, calculations using empirical formulae, and by using numerical methods based of physical models. Model testing and the use of empirical formulae are important to ship designers, whereas the scientific community is more interested in developing real physical models. Full scale testing is important both for verification of empirical models and physical models. The purpose of this presentation is to present studies on ice resistance of ships, which are based on direct calculation methods based on modelling of physical phenomena. Ice resistance of ships in two types of ice conditions are discussed: Ship ice resistance in level ice and ship ice resistance in a brash ice channel.
SIPW02 6th October 2017
09:00 to 09:45
Frank Thomas Smith Shear flow over patches of flexible surface and related near-surface interactions
Shear flow over a three-dimensional hydroelastic surface patch or patches is considered here, modelling the interactive effects encountered well within an incident atmospheric or sea-water boundary layer. The configuration has a finite patch or an array of patches of flexible surface which are sited in an otherwise quasi-fixed solid surface. The scaled viscous-inviscid response depends on the shear, the viscosity and therefore the vorticity, as well as ice-patch parameters and three-dimensionality. Related modelling of debris, particle and ice-shard movements involves fluid/body interaction. Analysis and computations on linear and nonlinear effects often leading to flow transition are to be described.
SIPW02 6th October 2017
09:45 to 10:30
Manish Tiwari Impact of supercooled droplets on nanoengineered surfaces
Ice formation is commonplace in nature and manmade applications and it also influences our lives positively and sometimes catastrophically. However, a clear understanding of ice formation, role of substrate/surface on which it forms are subjects of very vigorous  current research. Icing in dynamic conditions, such as freezing of a cold drop upon hitting a surface or freezing in the presence of airflow are even less understood, despite a few novel insights developed in the last five years. This presentation will start by summarising some open and closed questions on ice formation on surfaces using nucleation theory and its extensions and report on a number of experiments to this end, which use droplet/substrate system as a model. To this end we will discuss the role of surface nanoengineering and wettability control in controlling the ice nucleation. Insights into design of icephobic surfaces with exceptional ability to delay ice formation will also be shared. The role of environmental variables such as humidity an air flow will also be discussed. Next, for the majority of the presentation, we will consider the dynamic problem of droplet and jet impacting on such surfaces reaching speeds up to ~30 m/s and Weber numbers >10,000. Droplet supercooling and its effect on droplet impact dynamics will be analysed in detail. In addition, surface morphology needs and our initial results on surface durability testing will also be presented.
SIPW02 6th October 2017
11:00 to 11:45
Henrik Kalisch Fully dispersive nonlinear model equations for hydroelastic waves
SIPW02 6th October 2017
11:45 to 12:30
Ying Gou Experimental study on dead water resistance of ice floe in a two-layer fluid
Co-author: Bin Teng (University of Technology)

The dead water phenomenon is well known that when a boat is sailing on a two-layer fluid, there is an extra resistance due to the wave generating at the interface. Here, we investigate the dead water resistance of a ice floe instead of slender streamline body by three-dimensional towing experiments. The length-width ratio of ice floe is 1.5. The dimensionless ice floe draught d/h1 is varied from 0.5 to 1.0, where h1 is the upper layer depth. The Froude number Fr=U/c0 is in the range 0.3~1.3 (U towing speed, c0 the linear internal long wave speed). The experiment results show that dead water coefficient Cdw and function Cdw/(d/h1)2 attains a maximum at subcritical Froude number, Fr≈0.5~0.6, which is smaller than the previous results of slender ship. For relative small draughts, Cdw/(d/h1)2 depends on the Froude number only in the range close to critical speed (Fr>0.85), irrespective of the draught, which is same with the previous observations. But this conclusion is not applied for the case d/h1=1.0. The different variation tendency of Cdw/(d/h1)2 versus Fr is observed here. That means an extended study should be continued for deeper draught cases.
SIPW02 6th October 2017
13:30 to 14:15
Johannes E. M. Mosig Degrees of freedom in the marginal ice zone's wave--ice system
The marginal ice zones (MIZs) in both the Arctic and Southern Oceans play a key role in the Earth's climate system and the impact of sea ice on wave propagation is important to understand in order to create reliable wave forecasting models. To create efficient and accurate models of the MIZ's wave-ice system one must first identify the degrees of freedom that are relevant for such a model. In my PhD thesis and in this presentation, I will illuminate aspects of three commonly pursued paradigms: (i) floe models, where the degrees of freedom are comprised of individual ice floes; (ii) effective material models such as the one proposed by Wang and Shen (2010, dx.doi.org/10.1029/2009JC005591); and (iii) energy transport models, where the relevant degree of freedom is a single scalar field—the wave intensity—defined over the horizontal ocean domain.

Throughout this talk I will touch upon various mathematical and computational techniques which have very general applications, yet are rarely used by the wave and sea ice community.  Specifically, I use the method framework of generalized polynomial chaos to investigate the propagation of uncertainties in various models. Moreover, I attempt to derive an analytical relationship between local scale potential flow theory, and the large-scale transport equation description of the MIZ, using a multi-scale expansion and a Wigner transform of the amplitude envelope of a propagating wave package.

Supervisors: Vernon A. Squire, Fabien Montiel Publications: Mosig et al., Comparison of viscoelastic-type models for ocean wave attenuation in ice-covered seas, 2015, dx.doi.org/10.1002/2015JC010881 Mosig et al., Water wave scattering from a mass loading ice floe of random length using generalised polynomial chaos, dx.doi.org/10.1016/j.wavemoti.2016.09.005
SIPW02 6th October 2017
14:15 to 15:00
Usama Kadri On acoustic-gravity waves in arctic zones with elastic ice-sheets
We present an analytical solution of the boundary value problem of propagating acoustic-gravity waves generated in the ocean by earthquakes or ice-quakes in arctic zones. At the surface, we assume elastic ice-sheets of a variable thickness, and show that the propagating acoustic-gravity modes have different mode shape than originally derived by Ref. [1] for a rigid ice-sheet settings. Computationally, we couple the ice-sheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice-sheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depth-integrated equation valid for spatially slowly varying thickness of ice-sheet and water depth. Surprisingly, and unlike the free-surface setting, here it is found that the higher acoustic-gravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. ice-sheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acoustic-gravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation.
SIP 17th October 2017
15:00 to 16:30
David Schroeder Inter-annual variability and predictability of Arctic summer sea ice - review of previous years with focus on summer 2017
Observations give evidence that the Arctic sea ice is in decline. While some of the decline can be attributed to natural variability, Arctic sea ice is a prominent indicator of Climate Change. Is it possible to predict inter-annual variability of Arctic summer sea ice beyond the climate trend? Sources and limitations of sea ice predictability are discussed. Arctic summer sea ice can be accurately predicted using melt pond fraction in spring. This is due to a strong positive feedback mechanism: more ponds reduce the albedo; a lower albedo causes more melting; more melting increases pond fraction. The variability of Arctic sea ice during the last 5 years is analyzed including previous predictions and how they performed. What can we learn for sea ice modelling?
SIP 2nd November 2017
13:00 to 14:15
Beniamin Bogosel Parametric representation in shape optimization
In the numerical study of shape optimization problems the choice of the parametrization of shapes is an important aspect. An explicit parametrization can give direct access to geometric quantities related to the shape and can allow us to compute explicitly the cost function or use more precise techniques to solve the partial differential equations needed in the optimization process. In this talk I will show some examples where the use of a radial parametrization allows us to find precise approximations of solutions of some optimization problems regarding spectral quantities. In a second part I will show how using a parametrization based on the support function may lead to efficient ways of incorporating non-standard constraints, like diameter inequalities, constant-width or convexity into the optimization procedure. The results presented in the second part of the talk are in collaboration with Pedro Antunes.
SIPW03 6th November 2017
10:00 to 11:00
Erland Schulson Friction of Sea Ice
Friction of sea ice plays a fundamental role in a variety of geophysical and engineering scenarios. Examples include ridging and rafting, ice-induced loads on offshore structures and the physics of brittle compressive failure. In this paper attention is focused on the characteristics of static friction and frictional sliding of ice upon ice at velocities of around 0.1 m s-1 (~10 km/day) and lower, at homologous temperatures greater than around Th =0.85 (>-40 o C). The coefficients of both static and kinetic friction are described and then discussed in terms of the underlying physical processes. At root is creep deformation of asperities. Creep leads to an increase in contact area and thus to an increase in the coefficient of static friction with increasing time under load. Creep leads also to an increase in the coefficient of kinetic friction with increasing velocity at lower speeds. At higher speeds, localized melting of asperities sets in, via frictional heating, and this leads to a decrease in the kinetic coefficient with increasing velocity. Modeling indicates that the velocity that marks the transition scales as $V_t \propto a \Delta T^2$ where $a$ denotes asperity size and $\Delta T$, the difference in temperature between the melting point and the body of ice. Implications for sea ice mechanics are discussed.

SIPW03 6th November 2017
11:30 to 12:30
Paul Verlaan Ice-structure interaction in the Sakhalin-II (Sea of Okhotsk) and Kashagan (NE Caspian) project
In this presentation, it will be described which approach was taken to specify global and local ice loads for the structures in two different oil & gas projects in sub-Artic areas: the Sakhalin II project in the Sea of Okhotsk and the Kashagan project in NE Caspian Sea. In both projects, the approach was a combination of deterministic methods described in the different design codes, probabilistic methods and scale tests in an ice tank.  For the Sakhalin II project, global ice loads were particularly relevant for the design of the two multi-legged platforms (Piltun-B and Lunskoye-A). In contrast, in the NE Caspian, an accurate determination of the global ice loads was mainly relevant for design of the ice protection barriers rather than for design of the islands itself. Instead, much more attention was paid to specifying the risk of ice encroachment onto the islands.  In all cases, it was found that the limited amount of ice data often resulted in a conservative design with still considerable uncertainties in the design loads.
SIPW03 6th November 2017
13:30 to 14:30
David Cole Structure-property relationships for sea ice: Modeling and experimental validation
This talk addresses the constitutive behavior of sea ice, with a focus on the relationships between measurable physical properties and the elastic, anelastic and viscous components of strain. To accommodate attendees with a limited knowledge of sea ice, the presentation includes a brief overview of the microstructure and flaw structure of naturally occurring sea ice. Some attention is paid to the structure and mechanics of columnar and granular freshwater ice for completeness. The components of strain are quantified in terms of crystallographic characteristics (primarily c-axis orientation), dislocation density for the inelastic components, and temperature. The mechanisms of anelastic strain (e.g., time-dependent but recoverable) are associated with basal dislocation glide and grain boundary sliding. Viscous straining is quantified in terms of drag-controlled dislocation glide on the basal planes. It is shown that dislocation density exerts an overwhelming influence on the constitutive behavior of sea ice both at the scale of laboratory experiments (0.1 m) and in-situ experiments ( ≤ 30 m). Recent efforts to account for certain high temperature effects and differences between in-situ vs. in-vitro constitutive behavior of sea ice are described and the associated modifications to the published constitutive model are discussed. An analysis of existing cyclic loading and creep experiments makes it possible to identify the physical basis for the apparent increase in activation energy of inelastic behavior with proximity to the melting point. Additionally, brine drainage from specimens harvested for laboratory experiments is shown to cause a major discrepancy between the in-situ elastic response of warm sea ice vs. that found in laboratory experiments.
SIPW03 6th November 2017
14:30 to 15:30
Andrei Metrikine, Hayo Hendrikse Ice-induced vibrations of offshore structures: physics of the process, modelling and remaining challenges
SIPW03 6th November 2017
16:00 to 17:00
Aleksey Marchenko Thermo-mechanical loads of sea ice on structures
Thermally induced loads of ice on structures and shorelines occur due to thermal deformations of confined ice. Thermally induced stresses in the ice follow the temperature changes, depend on the coefficient of thermal expansion of ice and are reduced due to the relaxation. Temperature changes in sea ice occur due to conductive heat transfer characterized by specific heat capacity and thermal conductivity of ice and due to the advection of liquid brine depending on sea ice permeability. Coefficient of sea ice thermal expansion depends on the amount of liquid brine trapped in closed packets inside the ice. Proportion between the amounts of liquid brines trapped in closed packets and existing in permeable channels depends on the ice temperature and salinity. Relaxation and creep rheology of sea ice also depends on the temperature and ice structure.

Thermo-mechanical model of saline ice taking into account above described properties was recently formulated by Marchenko and Lishman (2017). The dependence of the coefficient of thermal expansion of saline ice from the temperature was reconstructed from the laboratory experiments. In the present work the model equations are used to estimate and compare the heat fluxes and thermal deformation of sea ice caused by the heat conduction and brine advection. Further the model is used for numerical simulations of ice loads on the cofferdam of coal quay in Kapp Amsterdam, Spitsbergen.

Field observations and records of the loads from sea ice confined inside the cofferdam were performed since 2013 (Marchenko et al, 2013; Wrangborg et al, 2015). Sea ice temperature was measured synchronously with the loads over entire ice thickness using thermistor string frozen into the ice. It was discovered that sea water brine migrates through the confined ice with thickness of 2-3 m under the influence of the water overpressure below the ice caused by semidiurnal tide. Horizontal ice loads on the cofferdam walls are also changed according to the semidiurnal cycle. Thermo-mechanical model of saline ice is used in numerical simulations of the observed phenomena by finite element method realized in Comsol Multiphysics software.
SIPW03 7th November 2017
09:00 to 10:00
Kaj Riska Theoretical modelling of ship-ice interaction
Ice action on ships occurs when a ship collides with an ice feature – be that level ice, ice floes or iceberg s. The total force acting on the ship depends on the motion of the ice feature and ship. The motion includes rigid body motions (in 6 DoF for ship and ice), elastic deformations of ship and ice and irreversible deformations (ice crushing and ship hull plastic deformation). In principle all these should be taken into account in modeling the collision and the total force. Several simplifications have been made and the lecture describes some of the modeling that has been carried out in order to determine the total collision force. An interaction exists also for local ice loading i.e. ice pressure. In this case the local deformation of the ship hull interacts with the deformation of ice. One example of this is given also in the lecture.
SIPW03 7th November 2017
10:00 to 11:00
Claude Daley Design and Assessment Methods for Ships in Ice
Design and assessment of ships in ice is a topic that concerns a wide range of people, from owners, to designers, builders, regulators and the insurance industry, with the public, the environment and the economy being impacted by arctic shipping risks. The methods that are being used to design and evaluate ice class ships have evolved over many decades and are currently continuing to change. In this discussion, the focus is on the steel structure of ice-going ships, including structurally important ice loads and the nature of the structural response.

As we seek to better understand the nature of the interaction between ships and ice, we are increasingly focusing on complex multi-body interactions and non-linear behaviours. In such situations, general solutions are not only not currently available, but may not be achievable at all. While we can assemble specific solutions, we must ask whether a general understanding of complex nonlinear systems is possible, and if so, what mathematics can we use to develop them?

Concern for structural ice loads has, until now, mainly focused on a single situation; the “design condition”. For that condition, the structure behaves linearly or pseudo-linearly. The “design” loads have been largely developed empirically, from a combination of measurement data and loads inferred from past successful practice.

While much of the current industrial and regulatory practice still employs relatively simple models of load and response, new sets of tools and approaches are taking shape and are being applied by the most sophisticated ship owners, builders and operators. These new approaches seek to directly model a growing set of complex issues and scenarios, with consequent improvements in the fidelity of ice loads and structural response. The growing computational power and improving simulation tools are enabling these developments. To illustrate these approaches, some of the author’s own efforts will be described.

One recent and developing technique is called safe speed analysis. This method involves modeling a wide variety of discrete ship-ice interaction cases, modelling the load and overload capacity of the vessel and then combining these results to produce a multi-parameter map of acceptable operations (speed, ice size, etc). The method makes use of available tools and solutions, including “Popov” type collision models (algebraic solutions of two-body collisions), and explicit dynamic finite element models (LS-Dyna) to capture interaction kinematics, contact and a full range of structural responses (ductility, dynamics, stability).

A second, but related technique is a model called GEM, which uses simple event solutions and simple equations of motion to model large scale operations of vessels in ice. GEM, while seeking a reasonable level of accuracy, focuses on high simulation speeds and practical decision support rather than on fidelity and universality.

After presenting these two methods, the presentation raises three mathematical challenges. The first challenge relates to the problem of interacting chaotic systems and wonders whether a calculus for such systems is possible. The second challenge questions the application of probabilistic design to ice class ships. The third challenge relates to the simulation of multi-body systems. Such systems are highly nonlinear and computationally costly to model. Could an asynchronous or quasi-synchronous timestep algorithm yield improvements in overall speed?
SIPW03 7th November 2017
11:30 to 12:30
Robert Bridges Influence of broken ice on marine operations – identification of important processes
SIPW03 7th November 2017
13:30 to 14:30
Alexander Korobkin Hydroelastic waves and their interaction with structures
Co-author: S. Malenica (BV), T. Khabakhpasheva (Lavrentyev Institute of Hydrodynamics)

Linear problems of hydroelastic wave diffraction by structures with vertical walls are studied for a circular cylinder frozen in ice cover of constant thickness and infinite extent. The water depth is constant. The ice plate is modelled by a thin elastic plate clamped to the surface of the cylinder. The cylinder is mounted at the sea bottom. One-dimensional incident hydroelastic wave of small amplitude propagates towards the cylinder and is diffracted on the cylinder.  Deflection of the ice plate and the bending stresses in it are determined by two methods: (a) using the integral Weber transform in radial direction, (b) using the vertical modes for the fluid of constant depth with the rigid bottom and elastic upper boundary. The solution by the second method is straightforward but we cannot prove that the solution is complete because the properties of the vertical modes are not known.  The solution by the Weber transform is more complicated but this solution is unique. We will show that these two solutions are identical. This result justifies the method of the vertical modes in the hydroelastic wave diffraction problems. For a circular cylinder the vertical-mode solution can be also justified by substitution. Different conditions at the contact line between the cylinder and the ice sheet are considered. The wave diffraction problem for broken ice is also considered. It is shown how the problem can be generalised to non-circular cylinders and interaction of several cylinders in ice.
SIPW03 7th November 2017
14:30 to 15:30
Yevgeny Aksenov Safer Operations in the Sea Ice-covered Oceans: The Tale of the Two Projects
INI Programme Mathematics of sea ice phenomena: SIPW03 (Ice-structures interactions) Safer operations in ice-covered oceans: The tale of the two projects Yevgeny Aksenov(1), Stefanie Rynders(1), Danny Feltham(2), Lucia Hosekova(2), Robert Marsh(3), Nicolaus Skrilis(3), Laurent Bertino(4) and Tim Williams(4) (1)National Oceanography Centre, UK (2)University of Reading, UK (3)University of Southampton, UK (4)Nansen Environmental and Remote Sensing Center (NERSC), Norway Contact: yka[at]noc.ac[dot]uk Increase in the Arctic offshore operations is driven easing of sea ice conditions and improving accessibility of the shipping routes. We present a review of the two projects, focus on the offshore and navigational safety in the high-latitude oceans. The projects develop analysis and forecasting technologies to provide key information for the maritime operations and marine information services. The projects bring together physical oceanography and the mathematics of fluid structure interaction and address the likely extreme loads on a selection of structures and ships, in a wide range of offshore environments, including pack ice areas and Marginal Ice Zones. The innovative capability develop in the project helps the integrated hindcasts and forecasts of ocean currents, tides and waves. We detail the data requirements and discuss existing and emerging datasets on ice thickness, ice drift and ice fragmentation and data on waves, tides, currents and icebergs). The study makes the assessment of the current and future states of the Arctic shipping, including, trans-Arctic navigation, regional Arctic shipping of commodities and transportation of Arctic natural resources. The approach uses sea ice drift, concentration and thickness fields from high-resolution model future projections in conjunction with the climate scenarios. For the study we acknowledge support from the EU FP7 Project ‘Ships and waves reaching Polar Regions (SWARP)’ and from the NERC UK Innovation Grant 'Safer Operations at Sea - Supported by Operational Simulations (SOS-SOS)'.
SIPW03 7th November 2017
16:00 to 17:00
Kevin Maki Nonlinear numerical modeling of impact loads of ship sections and floating ice
SIPW03 8th November 2017
09:00 to 10:00
Andrew Palmer How ought we to structure research so as to make progress in understanding ice interaction?
SIPW03 8th November 2017
10:00 to 11:00
Kenneth Johannessen Eik Effect of uncertainties in ice loading on design of Arctic installations
Co-author: Pavel Liferov (Statoil)

Statoil is operator in field developments offshore East Coast of Canada and in the Norwegian Barents Sea in waters were sea ice intrudes seldom (CA) or extremely rarely (NO). Both developments have in common that FPSOs will operate in open water but still need to consider ice loads as part of design. Norwegian laws require that the knowledge base is included as part of the risk definition. The consequence of this for Arctic Norwegian projects is that uncertainties in design basis shall be compensated with more robust solutions in order to keep risk at the same level as in non-arctic locations. Assessments done for the Johan Castberg project are presented with focus on possible consequences from using immature ice load models. The need for including ice exposure in load assessments and to relate loads to exceedance probability levels is highlighted.
SIPW03 8th November 2017
11:30 to 12:30
Devinder Sodhi Correlation of local ice forces across the width of a structure during ice-structure interaction
The concepts presented in this paper pertain to an ice floe moving against a wide structure, having an aspect ratio greater than 10, and are based on results of small-scale and medium-scale indentation tests as well as published data of measured ice forces on full-scale structures.

Data from indentation tests with tactile sensors at the ice-structure interface reveal that: (a) interactions at low ice speed produce ductile deformation of ice, creating a slowly expanding contact area until it covers 100% of the nominal contact area, and (b) interactions at intermediate and high ice speeds produce brittle failure of ice, resulting in the actual contact area to be less than the nominal contact area.

During interactions at intermediate and high speeds, brittle failure of ice creates uneven surface at the ice-structure interface, creating asperities at the ice front. When these asperities advance towards the structure, they generate contacts at a few isolated spots. During an ice-structure interaction, these contact areas expand under contact pressure with time, causing local ice forces to be generated at the ice-structure interface. The summation of all local forces at an instant in time is the global ice force.

The results of indentation tests with a segmented indentor and tactile sensor reveal a decrease in correlation of local ice forces across the width of a structure with increasing ice speed. This results in a decrease in variance of global effective pressure while the average global effective pressure remains in the range of local average effective pressure. These two effects are well supported by experimental results. The correlation of local ice forces is quantified by a correlation-length parameter, which decreases with increasing ice speed as per experimental data. These concepts of ice crushing process have been incorporated in a theoretical ice-structure-interaction model.
SIPW03 9th November 2017
09:00 to 10:00
Frank Thomas Smith Impacts, ice growth and related modelling
The presentation here by Frank Smith and Davide Bella is on interactions involved in impacts, ice formation and related phenomena. There are many such interactions. This mathematical-modelling research, motivated originally by the observed icing of airborne vehicles and the effects of storms, aims to address some of the following issues: first, distortion of water droplets in air flow, where two-way fluid interactions occur taking account of the small density and viscosity ratios; second, air-water interaction during the impact of a droplet onto a solid surface, including pre impact and post impact behaviour; third, ice growth soon after impact, where the interaction is between the ice shape and the water flow over it; fourth, related problems of dynamic fluid-body interaction concerning ice lumps impacting on a solid surface. More basic study of the ice growth within a single droplet on a solid surface will also be presented.
SIPW03 9th November 2017
10:00 to 11:00
Manish Tiwari Passive, nanoengineered anti-icing: An experimental perspective
In this presentation I will share results from some fundamental experiments focussed on investigating freezing of supercooled cold drops in contact with solid surfaces. A common theme running through the presentation will the need for precise surface nanotexturing and wettability control to control ice formation, ice adhesion and impalement resistance of surfaces subjected to impact by cold liquid objects. I will use experimental results to highlight a rational approach to design icephobic surfaces offering passive anti-icing property. Aspects of surface durability will be touched upon followed by a discussion on results from our preliminary work on impact of water drops on nanoengineered, iceohobic surfaces.
SIPW03 9th November 2017
13:30 to 14:30
Rocky Taylor Ice-induced vibrations in offshore structures: coupled dynamic ice-structure interactions over multiple scales
The design of fixed structures for operations in ice environments presents challenges, particularly in terms of determining appropriate levels of structural strengthening for extreme ice loads and accounting for potential ice-induced vibrations in design. The development of improved models of dynamic ice-structure interactions depends significantly on understanding the physics and mechanics of ice compressive failure to enable the effective modelling of ice loads and associated coupling with structural response. While the compressive failure of ice is highly complex, significant progress has been made in recent years in understanding and modelling salient aspects of ice failure during dynamic ice-structure interactions. In this lecture, emphasis is placed on processes associated with the formation and evolution of high-pressure zones (hpzs) and associated load-limiting mechanisms that occur during dynamic ice crushing failure. Recent advances in ice mechanics are discussed, a long with results of recent medium-scale laboratory tests focused on supporting the development of a probabilistic, multi-scale modelling framework as a basis for integrating advances in fundamental ice physics with full-scale ice loads on rigid and compliant structures.
SIPW03 9th November 2017
14:30 to 15:30
Dmitry Onishchenko Probabilistic aspects of multi-element systems failure
The problem of the determination of ice loads (or actions in ISO terminology) on offshore structures is essentially more difficult, from the methodological point of view, as compared with other environmental factors, such as wind, waves, currents. An engineer needs much more elaborated probabilistic approach for the ice case to determine the design values of ice loads, which yearly exceedance levels are set usually as 0,01 and lower. Reasons for this are well known: first, floating ice is diverse in shape, ice feature morphology is complicated and a number of ice structure parameters are not available for direct measuring at that, and second, in most cases ice load is a straightforward result of ice failure, a process that due to its physical nature has a very high level of internal uncertainty. In fact, it is reasonable to treat ice failure as a structural failure of a multi-element system, and in conditions when the individual elements have a non-trivial properties. The lecture, first, presents some basic ideas on probability aspects of multi-element systems failure that is closely related to the general subject of the reliability of structures. Then, with the help of a number of simple probabilistic models, the cases of level ice, ridges and icebergs impacts on offshore structures are presented. Certain attention i s given to a discussion on the overall reliability of the procedure of design ice load determination, which is closely connected with the accuracy of the probability distribution functions describing ice parameters and the adequacy of load equations.
SIPW03 9th November 2017
16:00 to 17:00
Kari Kolari Modelling Brittle Failure of Ice
The modeling of physics and mechanics of compressive failure is of importance in the ice-structure interaction modelling. Horizontal splitting of ice (termed spalling), has been observed in several ice-structure interaction experiments when drifting ice is failed by crushing in the interaction with vertical structure.

One of the greatest challenges of material failure analysis is the modelling of brittle failure. Materials like natural ice and rock are heterogeneous and crystalline, containing pores and flaws and other weaknesses. When these materials are subjected to compressive loading in the brittle regime, they are known to fail by splitting along the loading direction. Formation, growth and interaction of (micro)cracks due to material inhomogeneities and external force are considered to be the mechanism of brittle failure.

In this presentation, I will review three approaches applied in the modelling of brittle failure of ice: 1) Breakable/cohesive bond model; 2) Continuum damage mechanics (CDM) model, starting from Helmholz free energy; 3) WC-CMD-model, where the damage evolution is based on the observed micro-mechanism termed sliding wing crack mechanism.

The WC-CMD-model predicts axial splitting failure mode of granular ice under uniaxial and biaxial compression, and tensile splitting under tension. It also links grain size and strength of granular ice: the model is able to predict Hall-Petch relationship between grain diameter and strength, both under compression and tension. In addition, the model predicts experimentally observed increase in compressive strength with decrease in temperature.

SIPW03 10th November 2017
09:00 to 10:00
Mark Hopkins Using DEM to model ice sheets and structures
SIPW03 10th November 2017
10:00 to 11:00
Renate van Vliet Determining global ice loads on offshore structures
To design columns, foundations or mooring systems for offshore structures in areas exposed to ice, accurate estimates of global ice loads on the structure are required. In this presentation a comparison is made between the current practice of design of structures in ice and design of structures in waves and how loading is determined. The use of numerical models could increase the accuracy of ice load and structural response predictions, leading to reduced costs and risk of failure. Current use, gaps and ongoing development of numerical models for ice load prediction on structures are discussed.
SIPW03 10th November 2017
11:30 to 12:30
Jukka Tuhkuri, Arttu Polojarvi Discrete Element Simulation of Ice-Structure Interaction
Sea ice load on a marine structure is caused by the failure process of an ice feature against the structure. This failure process is affected by both, the structure and the ice, thus it is commonly called an ice-structure interaction process. Some ice failure processes comprise of large numbers of discrete failure events, which lead to formation of piles of ice blocks. Such failure process can be effectively studied by using the Discrete Element Method, DEM. As an example, when a continuous sea ice sheet is driven by the wind and current against a marine structure, the ice sheet gradually breaks into discrete blocks, which interact with each other and with the structure, and form a rubble pile against the structure. Our recent DEM simulations show that the force from the pushing ice sheet is transmitted to the structure through the rubble pile with chain-like groups of highly loaded ice blocks, force chains. The existence of force chains highlights the granular behavior of ic e rubble and calls for models that account for individual ice blocks. Other important problems where discrete ice blocks and their interactions have key roles, are the strength of sea ice ridges and rubble fields, and the interaction of ships and structures with ridges and rubble piles.
SIPW03 10th November 2017
13:30 to 14:30
Agnieszka Herman DEM modelling of wave-induced floe-floe (and floe-structure) collisions
In the marginal ice zone (MIZ), waves entering from the open ocean often induce collisions between neighboring ice floes. Due to limited observational data, it is not known to what degree wave-induced collisions contribute to the stress within the ice and to the dissipation of wave energy in MIZ. In this paper, wave-induced collisions between ice floes are analyzed with a numerical, discrete-element model. The model simulates surge motion of an ensemble of ice floes on a prescribed wave field. It is shown that the collision pattern depends on ice concentration, wave steepness, floe size relative to wavelength, floe-size distribution, as well as the restitution coefficient and drag between the ocean and the ice. For relatively large ice floes, the results are very sensitive to the formulation of wave forcing and ice–water drag. If the forcing correctly takes into account floe size relative to the wavelength, the model accurately reproduces surge RAOs of single floes, as well as accelerations and forces of floes impacting a structure.
SIPW03 10th November 2017
14:30 to 15:00
Izolda Sturova Generation of wave motion in fluid with inhomogeneous ice cover
The dynamic perturbations occurring in fluid and ice cover as a result of the action ofmechanical external force have been thoroughly studied in the linear treatment for aninfinitely extended homogeneous ice cover, which is modeled by a thin isotropicelastic plate floating on the surface of a fluid of constant depth. In reality, the icecover is not homogeneous, since it can cover not the entire upper boundary of a fluid,but only its part, and also there may be the cracks and the patches of ice-free water init. The effect of such complex boundary conditions on the wave motion is in the initialstage of the study.

We present a review of the solutions for several 2-D and 3-D problems. The timeharmonicproblem describing small oscillations (sway, heave and roll) of a horizontalcylinder is considered for four classes of hydroelastic system: i) a floating semiinfiniteelastic plate; ii) two semi-infinite elastic plates connected by the vertical andflexural rotational springs as a model of a partially frozen crack in an ice sheet; iii) afloating elastic platform of finite length; iv) two semi-infinite elastic plates separatedby a region of open water (polynya). The hydrodynamic load (added mass anddamping coefficients) and the amplitudes of vertical displacements of the free surfaceand elastic plates are calculated as functions of the cylinder oscillation frequency andthe location of the cylinder with respect to the plate edges.

The 3-D problem is considered for time-periodic external pressure and a load uniformly moving along the rectilinear edge of the ice cover. By analogy with the 2-D case, the first two classes of hydroelastic system are considered, as well as the effect of the solid vertical wall while the edge of the ice cover adjacent to the wall can be either clamped or free. In the problem of time-periodic external pressure, it is shown that for semi-infinite elastic plate contacting with free surface of water and for two non-identical semi-infinite plates, divided by crack, the directions of predominantwave propagation are allocated under some angle to the crack. In the case of two identical semi-infinite plates, divided by a crack, the edge wave guide mode is excited.The edge wave is most excited is the case of semi-infinite plate with a free edge near a solid vertical wall.

In the case of moving load, the 3-D pictures of generated waves in fluid and in ice cover are built for various speeds of motion. It is shown that in case of two identical semi-infinite plates, divided by a crack, two edge waveguide modes with different wave numbers exist for supercritical values of speed motion. For the vehicle moving with supercritical speed one mode is extending in front of moving load and other mode behind it. The wave forces acting on moving vehicle are investigated for various speeds of motion.
SIPW03 10th November 2017
15:00 to 15:30
Vladislav Miryaha Discontinuous Galerkin method for numerical simulation of ice flow impact on vertical cylinder offshore structure
Co-author - Prof. Igor B. Petrov

This talk describes an approach to numerical simulation of ice field impact on cylinder vertical offshore structure, as well as review of related complications.
Also it provides information on ice rheology, a continuous mechanics model used, which makes it possible to achieve a balance between accuracy and amount of computational resources needed. The description of the numerical method, and also some features of the simulation and techniques, which allow to overcome a number of difficulties associated with the resource-intensive calculations, are given. Typical destruction patterns of the ice fields and pressure distributions on structures are discussed.
SIP 14th November 2017
15:00 to 16:30
Guo Xiong Wu Interaction of wave with a body floating on a wide polynya
Guo Xiong Wu (University College London) Zhifu Li and Chunyan Ji (Jiangsu University of Science and Technology) A method based on wide spacing approximation is proposed for the interaction of water wave with a body floating on a polynya. The ice sheet is modelled as an elastic plate and fluid flow is described by the velocity potential theory. The solution procedure is constructed based on the assumption that when the distance between two disturbances to the free surface is sufficiently large, the interactions between them involve only the travelling waves caused by the disturbances and the effect of the evanescent waves is ignored. The solution for the problem can then be obtained from those for a floating body without ice sheet and for ice sheet/free surface without floating body. Both latter solutions have already been found previously and therefore there will be no additional effort in solution once the wide spacing approximation formulation is derived. Some explicit equations are derived to show zero reflection by the polynya, and peaks and troughs of the force and excited body motion. It is revealed that some of the peaks of the body motion are due to resonance while others are to the wave characters in the polynya. Presentation will cover other aspects of wave/ice/body interaction, including a body submerged below an ice sheet with a crack and hybrid numerical method.

SIP 20th November 2017
14:30 to 16:30
Alexander Korobkin Mixed boundary-value problems (tutorial)
Mbvps are introduced and explained. Theory of analytic functions is used to derive solution of a mbvp for two-dimensional Laplace equation through Cauchy-type integrals, Cauchy principal value integrals, characteristic function of the problem geometry, and conformal mapping of the solution domain. The tutorial is suitable for everybody, who is familiar with differentiation and integration, and curious about mathematical and numerical  features  of mbvps. The notes (48pp) are available on request.

SIP 27th November 2017
15:00 to 16:30
Malte Peter The suitability of the effective wavefield as a tool to predict wave attenuation over long distances
Ocean surface waves attenuate with distance travelled into the sea-ice covered ocean. This is reminiscent of the wave localisation phenomenon, which occurs in many branches of wave science. For an incident wave train propagating into a rough (randomly disordered) medium, wave localisation refers to exponential attenuation (on average) of the wave train in the rough medium. This talk is motivated by seeking efficient ways to calculate the attenuation rate as a function of the incident wave properties (frequency) and the properties of the given medium, including the statistical properties of the disorder. Effective media theory is an appealing way to approach the problem, as it provides analytical insight, circumventing the need to compute individual wave fields repeatedly for different realisations of the disorder, as well providing the opportunity for elegant mathematical analysis. I will present the theory alongside corresponding results and discuss the applicability of effective media theory for making predictions of wave attenuation over long distances.   This is joint work with L. G. Bennetts (Adelaide) and S. Rupprecht (Augsburg).

SIPW04 4th December 2017
10:00 to 11:00
Chris Petrich Growth process and structure of refrozen cracks in sea ice
SIPW04 4th December 2017
11:30 to 12:30
Sze Dai Pang Probabilistic Fracture Mechanics and Its Implications on Ice
Quasibrittle materials are materials in which the fracture process zone (FPZ) is not negligible as compared with the cross section dimension and encompass a wide variety of materials such as concrete, mortar, rocks, toughened ceramics, frozen sand, and ice also belongs to this class of materials. The size of the FPZ is typically 5-50 times the size of the dominant material inhomogeneity and for ice, it could be the grain size. For type 1 size effect which occurs in positive geometry structures failing at macrocrack initiation and is typical of flexural failures, the size effect is governed by Weibull statistics when the structure size dwarfs the size of the FPZ. When the structure size is comparable to the size of the FPZ, the probability distribution of the quasibrittle fracture can be described by a Gaussian core with a far-left Weibull tail. This is concluded from scaling laws derived from a hierarchical model of chains and bundles of representative volume elements starti ng from the atomic scale and include the effects of loading rate and temperature. The implications of probabilistic fracture mechanics on the strength of ice are investigated for different size of the ice sheet, varying strain rates and temperature effect.
SIPW04 4th December 2017
13:30 to 14:30
Chris Borstad Continuum damage models for fracturing and weakening of Antarctic ice shelves
Most of the Antarctic ice sheet drains to the ocean through floating ice shelves.  In many sectors of Antarctica, ice shelves are thinning due to oceanic or atmospheric warming, making them more susceptible to fracturing and even collapse.  Here I outline the different modes of ice shelf fracturing, including partial-thickness crevassing, through-thickness rifting, shear margin weakening, and the dominant mechanisms of iceberg calving. In the absence of a unifying damage framework capable of representing the diverse spatial and temporal scales of these mechanisms, I highlight two end-member damage models for particular cases.  The first is a fully elastic damage model, appropriate for representing the propagation of through-thickness rifts and tabular iceberg calving.  The second is a fully viscous damage model, appropriate for gradual weakening (especially in shear margins) of an ice shelf.  For the latter case, I present an adjoint-based inverse met hod for assimilating remote sensing data to infer a scalar damage variable over an ice shelf.  Results from a case study of the Larsen B ice shelf on the Antarctic Peninsula are used to inform the development of a damage evolution framework for application in ice sheet models.
SIPW04 4th December 2017
14:30 to 15:30
Roiy Sayag On the Formation and Evolution of Rifts in Ice Shelves
Rifts that form at the fronts of floating ice shelves are fractures that cut through the entire thickness of the ice. They are believed to be the precursor of calving, which accounts for a significant part in the mass loss of present ice sheets. Here we investigate the formation of rifts in ice shelves and their evolution by combining laboratory-scale experiments of ice sheets together with theoretical modeling. Experimentally we model the deformation of ice using a thin film of non-Newtonian fluid that is driven axisymmetrically by buoyancy. The viscous fluid intrudes a bath of an inviscid, denser fluid that represents the ocean. Consequently, the circular symmetry of the propagating front breaks up near the grounding line into a set of tongues with a characteristic wavelength that coarsens over time, a pattern that is reminiscent of some ice rifts. Theoretically, we model the formation of rifts as a hydrodynamic instability of a power-law fluid. Our model resolves the formation of rifts and the coarsening of the characteristic wavelength, and predicts coarsening transition times that are consistent with our experimental measurements. We discuss the instability mechanism and its implications.
SIPW04 4th December 2017
16:00 to 17:00
Erkan Oterkus Peridynamic Modelling of Ice Fracture
Despite of its advantages, utilization of the Arctic region for sailing brings new challenges due to its harsh environment. Therefore, ship structures must be designed to withstand ice loads in case of a collision between a ship and ice takes place. Although experimental studies can give invaluable information about ship-ice interactions, full scale tests are very costly to perform. Therefore, computer simulations can be a good alternative. Ice-structure interaction modelling is a very challenging process. First of all, ice material response depends on many different factors including applied-stress, strain-rate, temperature, grain-size, salinity, porosity and confining pressure. Furthermore, macro-scale modeling may not be sufficient to capture the full physical behaviour because the micro-scale effects may have a significant effect on macroscopic material behaviour. Hence, it is necessary to utilize a multi-scale methodology. In order to capture the macro-scale behaviour of ice, well-known Finite Element Method (FEM) has been used in various previous studies. Within FEM framework, various techniques can be used to model crack propagation such as cohesive zone models (CZM) and extended finite element method (XFEM). However, a universally accepted CZM failure model is not currently available and the crack propagation may have mesh dependency. Although, the mesh dependency problem can be overcome by XFEM, enrichment process may lead to an algebraic system with billions of unknowns which is difficult to solve numerically. Furthermore, FEM is based on classical continuum mechanics which does not have a length scale parameter and is incapable of capturing phenomenon at the micro-scale. Hence, other techniques should be utilized at the micro-scale and linked to FEM simulation. However, it is not straightforward to obtain a smooth transition between different approaches at different scales. By taking into account all these challenging issues, a state-of-the-art technique, peridynamics can be utilized for ice fracture modelling. Peridynamics is a non-classical (non-local) continuum mechanics formulation which is very suitable for failure analysis of materials due its mathematical structure. Cracks can occur naturally in the formulation and there is no need to impose an external crack growth law. Furthermore, due to its non-local character, it can capture the phenomenon at multiple scales.
SIPW04 5th December 2017
09:00 to 10:00
Kaj Riska Ice edge failure process
In the paper results from ice indentation tests are described. The tests were carried out to clarify the failure process of ice and also the loads caused by indentation into ice. The test results showed for the first time the nature of the brittle ice failure in caused a narrow high pressure zone (a line-like feature) transmitting the high pressures. The test results are described in some detail.

After looking at the test results, the implications on modeling ice failure are discussed. Especially the results of more recent tests are discussed and a phenomenological model for ice failure is given.
SIPW04 5th December 2017
10:00 to 11:00
Mao See Wu Crack nucleation in ice – a historical review and research challenges
This presentation focuses on crack nucleation in polycrystalline freshwater and saline ice. A historical review of the plausible nucleation mechanisms is provided, followed by a discussion of outstanding research challenges.

Since the late 1990s, several nucleation mechanisms have been investigated. These include: (i) dislocation pileup against obstacles such as grain boundaries, (ii) grain boundary sliding leading to displacement incompatibility at triple junctions, and (iii) elastic anisotropy of the hexagonal ice crystals giving rise to microstructural stresses which can nucleate cracks from precursors. For saline and sea ice, pressurized brine pockets are stress concentrators and likely crack nucleation sites.

The basal slip system is dominant in ice, and cracks may nucleate to relieve the strain heterogeneity arising from the strong plastic anisotropy of ice deformation. Furthermore, the interaction of various crack nucleation mechanisms under different conditions, e.g., temperature, grain size and texture, and the effect of time and loading rate on crack nucleation in viscoelastic ice, are issues that have received little attention. These are therefore research challenges that can be investigated in the future.
SIPW04 5th December 2017
11:30 to 12:30
Robert Gagnon The Physics of Ice Crushing Associated with Indentation and Impact
Ice crushing occurs in many contexts such as ice interaction with bridges, piers, ship hulls, offshore structures, rock beds under glaciers and ice-on-ice sliding/crushing interaction within glaciers and extraterrestrial ice masses (on Saturn’s moon Enceladus). In the cases of skate blades, sled runners and curling stones local crushing on ice asperities and/or small-scale ice unevenness, and due to gouging/plowing, occurs. In-situ imaging records from small and medium scale ice-crushing experiments show that repetitive spallation of ice from a relatively-intact hard zone in the central contact region produces a sawtooth load pattern, and most of the actual ice indentation occurs during the associated sharp drops in load. At least half of the load is borne on the hard zone, where the interface pressure is ~ 20-70 MPa. The rest of the load is borne on surrounding shattered spall debris, where the pressure is ~ 0-10 MPa. Spalling influences the evolution of hard-zone size and shape during the tests. The hard zones are regions where a thin squeeze-film slurry layer of pressurized melt and ice particles is present between the ice and the contacting surface. The viscous flow of the layer generates heat that accounts for the rapid-melting component of the removal of ice from the hard zones during ice crushing. A similar process occurs at ice-on-ice contact of fragments in the surrounding crushed-ice matrix as it extrudes away from the high-pressure zones. The melting accounts for the bulk of the energy dissipation and partly explains how an indentor can rapidly move forward on hard zones. The slurry layer thickness in small-scale lab tests is ~ 0.02 - 0.17 mm, where its liquid fraction is about 16%. The layer acts as a self-generating squeeze film that is powered by the energy supplied by the loading system. When ice crushing includes a sliding component the layer’s flow characteristics and high lubricity lead to very low friction coefficients, even on rough surfaces.
SIPW04 5th December 2017
13:30 to 14:30
Jukka Tuhkuri Deformation and failure of sea ice cover
Sea ice cover is moved by winds and currents. This motion leads to deformation and failure; though formation of leads in tension, and through ridging and rafting in compression. This presentation concentrates on the latter process. Ridges are elongated accumulations of broken sea ice. Rafting is another form of deformed ice. During rafting, one ice sheet overrides another ice sheet. Several models of ridging and rafting have been proposed: energy based models, models concentrating on the kinematics of the processes, and numerical models. Also laboratory experiments have been conducted to study ridging and rafting. In essence, all ridging and rafting initiates when two ice sheets are pushed together. In rafting, one ice sheet slides under another ice sheet, and we get two (or more) overlapped ice sheets. In ridging, ice blocks sequentially break of the ice sheets and form a ridge. Our experimental and numerical work suggests that all ridging initiates as rafting. Also, as the ice-ice friction coefficient is larger than zero, a rafting process will eventually turn into the formation of a pile of broken ice blocks, a ridge. Therefore, rafting and ridging should not be considered as two totally different deformation processes, but rather different stages of one process.
SIPW04 5th December 2017
14:30 to 15:30
Shunying Ji Breaking Pattern of Ice Cover during its Collision with Ship/Offshore Structures
Co-authors: Xue Long and Shuai Kong

Keywords
: Ice cover, Breaking pattern, Jacket platform, Ship hull, Discrete element method (DEM),
SIPW04 5th December 2017
16:00 to 17:00
Hayley Shen Integrating Elastic and Viscous Properties of Ice for Ocean Wave Propagation
As a material, ice covers are mixtures of various forms of solid, water (with or without salt), and air. They are heterogeneous under all scales. A number of mathematical models have been proposed to describe the dispersive/dissipative property of an ice cover. In this talk we examine one of such models that integrates both the energy storage and dissipation capability of an ice cover. The mathematical complexity resulted in this very simple looking model, and its skill of predicting spectral dissipation will be discussed.
SIPW04 6th December 2017
09:00 to 10:00
Steven Daly River Ice Breakup
Breakup transforms an ice-covered river into an open river. Two ideal forms of breakup bracket the types of breakup commonly found throughout most of the globe. At one extreme is thermal breakup. During an ideal thermal breakup, the river ice cover deteriorates and melts in place, with no increase in flow and little or no ice movement. At the other extreme is the more complex and less understood mechanical breakup (also referred to as a dynamic breakup). Mechanical breakup requires no deterioration of the ice cover, but rather results from an increase in flow entering the river. The increase in flow induces stresses in the cover, and the stresses in turn cause cracks and the ultimate fragmentation of the ice cover into pieces that are carried by the channel flow. Ice jams take place at locations where the ice fragments stop; severe and sudden hydraulic transients can result when these ice jams form or when they release. This presentation will focus on mechanical breakup and the historical evolution of our understanding of this topic. The presentation will include discussions of ice cover formation and the typical resulting ice structure, wave-ice interaction, the physics of the cracking, and the current status of our understanding of breakup.
SIPW04 6th December 2017
10:00 to 11:00
Dany Dumont Sea ice break-up in the marginal ice zone
Sea ice is a granular material composed of interacting elements, called floes, of different and evolving sizes and shapes. Contemporary numerical models of sea ice, although incorporating aspects of granular material dynamics, do not realistically represent the evolution of floe size distribution, which is affected by and upon which depend a myriad of dynamical and thermodynamical processes. Although this problem is theoretically, numerically and experimentally challenging, there has been significant progress over the past decade thanks to many international collaborative efforts, especially through revisiting marginal ice zone dynamics where surface gravity waves exert a strong control on floe size. This presentation will provide an overview of the theoretical and experimental knowledge on sea ice break-up and floe size distribution and will discuss how this topic is handled analytically in models.
SIPW04 6th December 2017
11:30 to 12:30
Hung Tao Shen Issues on modeling river ice dynamics
The presence of ice in rivers is an important phenomenon to be considered in the development of water resources in cold regions. Ice formation can affect the design, operation, and maintenance of hydraulic engineering facilities in cold regions. River ice phenomena involve complex interactions between hydrodynamic, mechanical, and thermal processes, as well as the ambient hydro-meteorological conditions and channel morphology. This presentation will discuss the current state of knowledge and unresolved issues on modeling river ice dynamics and the associated thermal processes. These issues include ice jam formation and release during freeze up and breakup, ice cover breakup, frazil ice evolution, and anchor ice formation and release. The possible similarities between these river ice phenomena and sea ice will be discussed.

Keywords: River ice, freeze up, ice jams, breakup, hydrodynamics, mathematical modeling
SIP 6th December 2017
14:30 to 15:30
Gennady Mishuris Impact of the hydraulically induced shear stress on hydraulic fracture
A revised model of the hydraulic fracture (HF) formulation [1] that accounts for the hydraulically induced shear stress at the crack faces is discussed. It is shown that, due to the order of the tip singularity of the hydraulic shear stress, this component of the load cannot be omitted in the analysis. The amended crack propagation criterion based on the critical value of the energy release rate is derived. A new parameter, the fluid shear stress intensity factor, is introduced and has proved to play an important role in the HF process. It is also shown that the shear stress induced by viscous fluid at the crack faces influences the crack propagation direction in the mixed mode fracture [2]. Numerical simulations have highlighted advantages of the revised HF model. In particular, the small toughness regime is no longer presents a significant computational challenge. The modified formulation opens new ways not only to analyse the physical phenomenon of HF, but for improving the reliability and efficiency of its numerical simulation as well. [1] Wrobel, M., Mishuris, G., Piccolroaz, A. 2017. Energy release rate in hydraulic fracture: Can we neglect an impact of the hydraulically induced shear stress? International Journal of Engineering Science. 111 pp. 28-51. [2] Perkowska, M., Piccolroaz, A., Wrobel, M., Mishuris, G. 2017. Redirection of a crack driven by viscous fluid. International Journal of Engineering Science 121 pp. 182-193.

SIP 6th December 2017
15:30 to 16:30
Michael Nieves Potential new pathways in modelling sea ice phenomena coming from the analysis of multiscale solids with defects
In this talk, we discuss two methods used in the modelling of materials with defects at different scales.   The first, known as the method of mesoscale asymptotic approximations [1],  is appropriate for the modelling of granular materials. In particular, we discuss the approximation of solutions to a particular class of transmission problems in solids containing clusters of many small inclusions, which can interact with each other [2]. The asymptotics are supplied with remainder estimates that are rigorously justified.    The second method concerns the dynamic failure of structured materials, commonly used in understanding the phenomena involved at multiple scales in the fracture of solids. The subject has been explored in the last 30 years for a variety of mass-spring systems [3].  Here, we take a different approach and consider faults propagating through periodic mass-beam systems [4, 5], which are more commonly found in civil engineering applications such as long rooftops, bridges and pipeline systems. We give a summary of analytical results, based on the Fourier transform and the Wiener-Hopf technique, concerning the dynamic behaviour of the structure during the failure.   Numerical simulations demonstrate the effectiveness of both approaches. It is envisaged that both techniques may find a new home in the modelling of phenomena associated with the behaviour of sea ice.   References:  [1] V. Maz’ya, A. Movchan and M. Nieves, (2013): Green’s Kernels and Meso-Scale Approximations in Perforated Domains, Lecture Notes in Mathematics 2077, Springer. [2] M.J. Nieves, (2017): Asymptotic analysis of solutions to transmission problems in solids with many inclusions, SIAM J. Appl. Math. 77 (4), 1417-1443. [3] L.I. Slepyan,  (2002): Models and Phenomena in Fracture Mechanics, Foundations of Engineering Mechanics, Springer. [4] M.J. Nieves, G.S. Mishuris, L.I. Slepyan, (2016): Analysis of dynamic damage propagation in discrete beam structures, Int. J. Solids Struct. 97-98, 699-713.  [5] M.J. Nieves, G.S. Mishuris, L.I. Slepyan, (2017): Transient wave in a transformable periodic flexural structure, Int. J. Solids Struct. 112, 185-208

SIPW04 7th December 2017
09:00 to 10:00
Victor Tsai Hydrofracture Propagation from Supraglacial Lake Drainage
Seasonal melt that forms at the surface of the Greenland Ice Sheet often eventually finds its way to the bed of the ice sheet, where it can have a significant effect on ice sheet dynamics. However, the way in which meltwater pathways from the surface to the bed are formed and maintained is not well understood. In this presentation, I will discuss the mechanics of hydrofracture, through which initial surface-to-bed connections are thought to be made. Hydrofracture of liquid water through its solid phase has unique mechanics, partly due to the low viscosity and turbulence of water, the higher density of water than ice, the melting of ice that occurs with viscous dissipation of turbulent energy, and the viscoelastic deformation of ice. A simplified model will be presented that describes the essential aspects of such hydrofracture, and the implications for glacier dynamics will be explained.
SIPW04 7th December 2017
10:00 to 11:00
Peter Sammonds Micromechanics of sea ice frictional slip from test basin scale experiments
Co-authors: Daniel Hatton and Daniel Feltham

We have performed high-resolution double-direct shear friction experiments on saline ice floes in the HSVA environmental test basin. The frictional motion was predominantly stick-slip.  Shear stresses, normal stresses, local strains and slip displacement were measured along the sliding faults, and acoustic emissions were monitored. High resolution measurements during a single stick- slip cycle at several positions along the fault allowed us to identify two phases of frictional slip: a nucleation phase, where a nucleation zone begins to slip before the rest of the fault, and a propagation phase when the entire fault is slipping. We employed a constitutive relation for frictional slip derived from the physics of asperity-asperity contact. We find our experimental data conform reasonably with this frictional law once slip weakening is introduced.  We deduce the interfacial faults failed in the stick-slip cycle through the process of brittle failure of asperities in shear, and at higher velocities, frictional heating, localized surface melting and hydrodynamic lubrication.
SIPW04 7th December 2017
11:30 to 12:30
Erland Schulson Cracks in ice and their role in brittle compressive failure
Cracks--new and old, short and long-- are ubiquitous features within the arctic sea ice cover. How they form and the role they play in mechanical behavior are important questions in ice mechanics. In this presentation, emphasis will be placed on brittle compressive failure. There, cracks preferentially oriented with respect to the applied stress state can slide intermittently across opposing surfaces in contact, activating in the process deformation mechanisms that can account for a number of observations/characteristics of brittle compressive failure on scales small and large. One such scale-independent mechanism is the wing-crack cum comb-crack mechanism: it can account for the axial splitting and shear faulting modes of terminal failure, conjugate faulting, brittle compressive strength and, upon consideration of crack-tip creep, the transition from brittle to ductile behavior. Application of confining stress above a critical level, set solely by the coefficient of kinetic friction, suppresses frictional sliding and activates, given a sufficiently high strain rate and triaxial confinement, a brittle-like mode of plastic failure governed by the different mechanism of adiabatic heating and dynamic recrystallization. These mechanisms will be described and questions arising addressed.

SIPW04 7th December 2017
13:30 to 14:30
Jerome Weiss Coulomb’s mechanics of sea ice: From geophysical evidences to experimental modeling
In 1773, Charles Augustin de Coulomb 1 proposed his celebrated failure criterion, postulating that under shear and compressive stress states failure occurs along a fault plane when the applied shear stress acting on that plane overcomes a resistance made of two parts of different nature: a cohesion τ_0, and a frictional resistance proportional to the normal pressure σ_n. The relevance of the Coulomb’s “theory” of failure for faulting and earthquake mechanics was recognized more than one century ago2, and remains nowadays a major tool of interpretation in civil engineering, the mechanics of granular media, and solid Earth geophysics. Its application to sea ice mechanics is much more recent. Satellite imagery3, 4 as well as in-situ stress data5 revealed that most of Artic sea ice pack deformation occurs through the activation of Coulomb’s faults. Many questions remain however, such as the partitioning between cohesion and friction in the resistance of sea ice faults, the competition between faulting and healing (through refreezing) in setting the long-term dynamics of faulting, or sliding velocity effects. To explore these questions, an analog experiment was recently developed in Grenoble, consisting of a thin ice layer sitting on top of a water tank and mechanically deformed at various rates with a circular Couette-like geometry6. This allowed sliding along a circular fault surface over arbitrarily large slip distances, and analyzing the competition between faulting and healing from the control of the rotation velocity and the air temperature of the cold room. The results marked out the relevance of Coulomb’s mechanics towards small normal stresses, explored the role of mechanical forcing and air temperature on ice faults long-term dynamics, and may represent a benchmark for the future development of sea ice mechanical models.
SIPW04 7th December 2017
14:30 to 15:30
Sveinung Loset Global Ice Fracture Experiments at Spitsbergen and Its Impact on Numerical Simulation of Ice Actions
Co-author: Wenjun Lu (Norwegian University of Science and Technology)

The ice cover in the Arctic is both diminishing in areal extent and thinning. This leads to a situation where gravity waves are more prone to break up the ice cover into floe ice, and penetrate deeper into the ice fields in the Arctic. When this type of broken ice is interacting with offshore structures and ships, global fracturing of small or larger floes will be a major part of the interaction process and should be considered when either physically or numerically simulating the interaction process. An ice floe may fracture in different patterns. For example, it can be local bending failure or global splitting failure depending on the contact properties, geometry and confinement of the ice floe. Modelling these different fracture patterns as a natural outcome of numerical simulations is rather challenging. This is mainly because the effects of crack propagation, crack branching, multi fracturing modes and eventual fragmentation within a solid material are still questions to be answered by the on-going research in the Computational Mechanic community. In addition, the scale fracture properties of sea ice are still under discussions. To remedy some of these questions for ice we have conducted a number of physical fracture experiments at Spitsbergen during the winter of 2015-2017. The outcome of this research will be reported as well as the impact on numerical simulations of ice-structure interaction.
SIPW04 8th December 2017
09:00 to 10:00
Veronique Dansereau A Maxwell-Elasto-Brittle model for the drift and deformation of sea ice
In recent years, the viscous hypothesis and other underlying physical assumptions of the viscous-plastic (VP) rheology widely used in current climate and operational models have been revisited and found to be inconsistent with the observed mechanical behaviour of sea ice. Other studies have suggested that while the VP model can represent the mean global drift of sea ice with a certain level of accuracy, it fails at reproducing some key observed properties of sea ice deformation. We developed a new mechanical model, named Maxwell-Elasto-Brittle, as an alternative to the VP rheology in the view of accurately reproducing the drift and deformation of the ice cover in continuum sea ice models. The model builds on a damage mechanics framework used for ice and rocks. A viscous-like relaxation term is added to a linear-elastic constitutive relationship together with an effective viscosity that evolves with the local level of damage of the material, like its elastic modulus. This framework allows the internal stress to dissipate in large, permanent deformations along faults, or leads, once the material is highly damaged, while reproducing the small deformations associated with the fracturing process and retaining the memory of elastic deformations over relatively low damage areas. A healing mechanism counterbalances the effects of damaging over large time scales.

Idealized simulations have confirmed that the Maxwell-EB model reproduces the important characteristics of sea ice mechanics revealed by the analyses of available ice buoy and satellite data: the anisotropy of the deformation, the strain localization and intermittency, as well as the associated scaling laws. Sensitivity analyses show that the model, with few independent variables, can represent a large range of mechanical behaviours, with both the persistence of creeping leads and the activation of new leads with different shapes and orientations. Realistic simulations will be presented, in particular, simulations of the flow of ice through Nares Strait. These will demonstrate that the model reproduces the formation of stable ice bridges as well as the stoppage of the flow, a common phenomenon within numerous channels of the Arctic. In agreement with observations, the propagation of damage along narrow arch-like kinematic features, the discontinuities in the velocity field across these features, defining floes, and the eventual opening of polynyas downstream of the Strait are all represented.
SIPW04 8th December 2017
10:00 to 11:00
Kara Peterson Evaluation of an Elastic-Decohesive Rheology for Sea Ice
Satellite data obtained over the last couple decades have provided a wealth of information on sea ice motion and deformation for use in model comparison and validation. The data clearly show that ice deformation is focused along narrow linear features, which we would like to capture accurately in models. In this talk we describe an elastic-decohesive rheology that explicitly includes discontinuities in the deformation field to represent sea ice cracks. We compare results from an implementation in the UNM MPM sea ice model and a preliminary implementation in the LANL CICE model with RADARSAT Geophysical Processor System deformation data and results from the standard elastic-viscous-plastic rheology.
SIPW04 8th December 2017
11:30 to 12:30
Han Duc Tran An anisotropic elastic-decohesive constitutive relation for sea ice
Co-authors: Deborah L. Sulsky (University of New Mexico), Howard L. Schreyer (University of New Mexico)

When leads in sea ice expose warm underlying ocean to the frigid winter atmosphere, new ice is formed rapidly by freezing ocean water. Then convergence or closing of the pack ice forces the new ice in leads to pile up into ridges and to be forced down into keels. Together with thermodynamic growth, these mechanical processes shape the thickness distribution of the ice cover, and impact the overall strength of pack ice. Specifically, the deformation and strength of ice are not isotropic but vary with the thickness and orientation of the categories. To reflect these facts, we develop an anisotropic constitutive model for sea ice consisting an oriented thickness distribution. The model describes anisotropically mechanical responses in both elastic and failure regimes. In the elastic regime, the constitutive relation implicitly reflects the strong and weak directions of the pack ice depending on the distribution of thin ice and thicker ice. The existence of open water, a special case of thin ice, is also reflected in the elastic constitutive relation in which the free-traction condition is satisfied. In the failure regime, the model predicts when an initial failure, i.e. a microcrack, occurs and what the direction of the failure is. The evolution of a microcrack to a macrocrack, i.e. when free-traction crack surfaces are completely formed, is also modeled, and a numerical procedure is proposed to determine the width of cracks. Sample paths in stress space are used to illustrate how the model can simulate failure. Several examples of failure surfaces are presented to describe the behavior of ice when varying thickness distributions. The model predictions are also illustrated and compared with previous modeling efforts by examining regions under idealized loading.
SIPW04 8th December 2017
13:30 to 14:30
Daniel Feltham Anisotropic sea ice mechanics
Observations show that the sea ice pack is heterogeneous and heavily flawed. Deformation in response to wind and ocean stresses occurs discontinuously at existing areas of weakness or through the formation of new damaged zones. The orientation of the damaged zones is affected by existing weaknesses in the pack and the orientation of the applied stresses. The orientation of these zones, in turn, affect the direction and magnitude of internal ice stresses. I describe work motivated by the need to represent the dependence of sea ice stress on orientation of existing weaknesses in continuum climate sea ice models. I will describe some discrete element simulation results that help provide understanding, and the form of an anisotropic continuum sea ice model designed to be used in climate models. I will present simulations highlighting the operation and features of this anisotropic rheology in climate-type sea ice simulations.
SIPW04 8th December 2017
14:30 to 15:30
John Dempsey Fracture Mechanics Applied To Ice Ih
The initial reluctance to adopt the fracture mechanics approach in ice mechanics and ice dynamics will be examined. The fundamentals of fracture mechanics and different fracture criteria will be reviewed. The relationship between models that idealize the crack-tip as a singular stress field and those that include a cohesive zone will be explored. Experimental values of material parameters determined in the laboratory and in the field will be examined. Time dependent and material effects on crack growth initiation and during crack propagation will be discussed. The limitations of fracture mechanics will be explored.
SIP 12th December 2017
11:30 to 12:30
Vitaliy Zemlyak Experimental modelling of waves in ice cover
SIP 13th December 2017
11:00 to 11:30
Anna Chernyshova Two- and three-dimensional effects in spatial and temporal evolution of water waves excited by wind and generated mechanically
SIP 13th December 2017
11:30 to 12:30
Pavel Chernyshov Inversion of waves and current profiles using X-band radar in coastal zone