Coherent Vorticity Simulation of Three-Dimensional Forced Homogeneous Isotropic Turbulence

Abstract

Coherent vorticity simulation (CVS) is a multiscale method to compute incompressible turbulent flows based on the wavelet filtered Navier–Stokes equations. At each time step the vorticity field is decomposed into two orthogonal components using an orthogonal wavelet basis: the coherent vorticity, corresponding to the coefficients whose modulus is larger than a threshold, and the remaining incoherent vorticity. The threshold value only depends on the total enstrophy, which evolves in time, and on the maximal resolution, which remains constant. The induced coherent velocity is computed from the coherent vorticity using the Biot–Savart kernel. To compute the flow evolution one only retains the coherent wavelet coefficients and some of their neighbors in space, scale, and direction, which define the safety zone. Two different strategies are studied to minimize at each time step the number of degrees of freedom to be computed, either by increasing the threshold value or by reducing the width of the safety zone. Their efficiency is compared for a three-dimensional forced homogeneous isotropic turbulent flow at initial Taylor microscale Reynolds number . The quality of the results is assessed in comparison to a direct numerical simulation of the same flow. It is found that, as long as a safety zone is present, CVS well preserves the statistical predictability of the turbulent flow (even the vorticity and velocity probability distribution functions) with a reduced number of degrees of freedom.