Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows

Abstract

A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified asvT=(Csδ)2(|S|—|〈S〉|): the magnitude of the mean shear |〈S〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor |S|;CSis the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbersReτ= 395 andReτ= 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.