From single-scale turbulence models to multiple-scale and subgrid-scale models by Fourier transform

Abstract

A theoretical method based on mathematical physics formalism that allows transposition of turbulence modeling methods from URANS (unsteady Reynolds averaged Navier–Stokes) models, to multiple-scale models and large eddy simulations (LES) is presented. The method is based on the spectral Fourier transform of the dynamic equation of the two-point fluctuating velocity correlations with an extension to the case of non-homogenous turbulence. The resulting equation describes the evolution of the spectral velocity correlation tensor in wave vector space. Then, we show that the full wave number integration of the spectral equation allows one to recover usual one-point statistical closure whereas the partial integration based on spectrum splitting gives rise to partial integrated transport models (PITM). This latter approach, depending on the type of spectral partitioning used, can yield either a statistical multiple-scale model or subfilter transport models used in LES or hybrid methods, providing some appropriate approximations are made. Closure hypotheses underlying these models are then discussed by reference to physical considerations with emphasis on identification of tensorial fluxes that represent turbulent energy transfer or dissipation. Some experiments such as the homogeneous axisymmetric contraction, the decay of isotropic turbulence, the pulsed turbulent channel flow and a wall injection induced flow are then considered as typical possible applications for illustrating the potentials of these models.