Abstract

Coherent Vortex Simulation (CVS) is based on the wavelet filtered Navier-Stokes equations, where at each instant the turbulent flow is split into two orthogonal contributions: the coherent flow made of vortices which is kept, and the incoherent flow made of the background fluctuations which is discarded. The CVS filter is based on an orthogonal wavelet decomposition of the vorticity field where only the wavelet coefficients whose modulus is larger than a given threshold are kept. The value of the threshold depends only on the total enstrophy and on the numerical resolution used to represent the flow.

The CVS filter has already been applied to 2D [Farge, Schneider and Kevlahan in Phys. Fluids 11(8) 1999] and 3D [Farge, Pellegrino and Schneider in Phys. Rev. Lett. 87(55) 2001, Farge et al. in Phys. Fluids 15(10) 2003, Okamoto et al. in Phys. Fluids 19 2007] turbulent flows, where it has been shown that only few wavelet coefficients (from 0.7% for 256^{2 up to 2.6% for 2046}3 resolution) are sufficient to represent the coherent flow which preserves the vorticity and velocity PDFs, the energy spectrum and the nonlinear transfers all along the inertial range.

We will analyze the time evolution of a decaying homogeneous isotropic turbulent flow, by applying the CVS filter at each time step of a Direct Numerical Simulation (DNS). We will compare the Eulerian and Lagrangian mixing properties of the total, coherent and incoherent flows by studying how they advect a passive tracer and many particles during several eddy turn-over times. We will quantify the mixing properties of coherent and incoherent flows and show that efficient mixing is due to the transport by vortices, while the incoherent contribution is much weaker and only diffusive.

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