Abstract
The influence of rotation on the structure and dynamics of sheared turbulence is investigated using a series of direct numerical simulations (DNS). We consider a mean flow in the downstream direction which has a constant shear in the vertical direction. The rotation is applied to the system in the positive spanwise direction, i.e., perpendicular to the plane of shear and parallel to the mean vorticity. The 3D Navier-Stokes equations are solved using a spectral scheme with 256^3 modes for the space integration, and a fourth order Runge-Kutta scheme for the time integration. Five cases are considered: turbulent shear flow without rotation, with moderate rotation, and with strong rotation, where the rotation configuration is either parallel or anti-parallel to the mean flow vorticity.
For moderate rotation rates, we found that an anti-parallel configuration increases the growth of the turbulent kinetic energy, while a parallel configuration reduces it, as compared to the non-rotating case. For strong rotation rates, we observe that energy decays, linear effects dominate the flow, and the vorticity PDFs tend to become Gaussian. Visualizations of the vorticity field show that the inclination angle of the vortical structures depends on the rotation rate and orientation.
The CVS filter [1], which is based on the orthogonal wavelet [2] decomposition of vorticity, is applied to split the flow into coherent and incoherent contributions. It was found that the coherent contribution preserves the vortical structures using only a few percent of the degrees of freedom. In contrast, the incoherent contribution is structureless and of purely dissipative nature. With increasing rotation rates, the number of wavelet modes representing the coherent vortices decreases, which indicates an increased coherency of the flow. We integrate separately the coherent and the incoherent flow, and we show that the former preserves the temporal dynamics of the total flow, while the latter is of dissipative nature [3].
Acknowledgments:
We thankfully acknowledge financial support from ANR, project M2TFP.
References:
[1] Marie Farge, Giulio Pellegrino and Kai Schneider, 2001 Coherent vortex extraction in 3D turbulent flows using orthogonal wavelets Phys. Rev. Lett., 87(55), 054501
[2] Marie Farge, 1992 Wavelet transforms and their applications to turbulence Ann. Rev. Fluid Mech., 24, 395-457
[3] Frank G. Jacobitz, Lukas Liechtenstein, Kai Schneider and Marie Farge, 2008 On the structure and dynamics of sheared and rotating turbulence: direct numerical simulation and wavelet-based coherent vortex extraction Phys. Fluids, 20 (4), 045103
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