Spectral large-eddy simulations and vortex dynamics in turbulence

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 tie existence of a k(4) infrared backscatter in the kinetic-energy spectrum, and predict a new k(2) 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 Lambda-cortices which are carried a 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.