From two-point closures of isotropic turbulence to LES of shear flows

We first recall the EDQNM two-point closure approach of three-dimensional i sotropic turbulence. It allows in particular prediction of the infrared kin etic-energy dynamics (with a k(4) backscatter) and the associated time-deca y law of kinetic-energy, useful in particular for one-point closure modelli ng. Afterwards, we show how the spectral eddy viscosity concept may be used for large-eddy simulations: we introduce the plateau-peak model and the sp ectral-dynamic models. They are applied to decaying isotropic turbulence, a nd allow recovery of the EDQNM infrared energy dynamics. A new infrared k(2 ) law for the pressure spectrum, predicted by the closure, is also well ver ified. Assuming that subgrid scales are not too far from isotropy, the spectral-dy namic model is applied to the channel flow at h(+) = 390, with statistics i n very good agreement with DNS, while reducing considerably the computation al time. We study with the aid of DNS and LES the case of the channel rotat ing about an axis of spanwise direction. The calculations allow to recover the universal linear behaviour of the mean velocity profile, with a local R ossby number equal to -1. We present also LES (using the Grenoble Filtered Structure-Function Model), of a turbulent boundary layer passing over a cavity. Finally, we make some remarks on the future of LES for industrial applications.