Spectral Large-Eddy Simulations and Vortex Dynamics in Turbulence.

Abstract

We present a point of view of large-eddy simulations(LES)in Fourier space, where the eddy coefficients are expressed thanks to a two-point spectral closure of isotropic turbulence, the EDQNM theory. Returning to real space, this leads to models of the structure-function family(plain, selective or filtered). These models are applied with success to predict the statistical distributions and coherent-vortex dynamics for a wide variety of turbulent flows. In three-dimensional decaying isotropic turbulence, we confirm the existence of a κ4 infrared backscatter in the kinetic-energy spectrum, and predict a new κ2 law for the pressure spectrum in this range. In the mixing layer(temporal or spatial), we show how to manipulate the topology of Kelvin-Helmholtz vortices, from quasi two-dimensionality to helical pairing. The latter vortex organization is found in a backward-facing step just behind the step, and yields big staggered Λ-vortices which are carried away downstream. In a developed turbulent boundary layer, coherent vortices are hairpins generated above the low-speed streaks by a secondary Kelvin-Helmholtz instability. Afterwards, we consider LES of compressible turbulence, studied with Favre averages, and where the introduction of a macro-temperature and a macro-pressure simplifies greatly the problem. Finally, we show in rotating shear flows(free or wall bounded, axis of rotation in the spanwise direction)a universal behaviour of the mean velocity which becomes linear in certain anticyclonic regions.