Effects of molecular diffusion on the subgrid-scale modeling of passive scalars

Abstract

The spectral eddy-viscosity and eddy-diffusivity closures derived from the eddy-damped quasinormal Markovian (EDQNM) theory, and one of its physical space counterparts, i.e., the structure function model [Métais and Lesieur, J. Fluid Mech. 239, 157 (1992)], are revisited to account for molecular viscosity and diffusivity effects. The subgrid-scale Schmidt number (usually set to Sct≈0.6) is analytically derived from the EDQNM theory and shown to be Reynolds number dependent, a property of utmost importance for flows involving scalar transport at moderate Reynolds numbers or during the transition to turbulence. A priori tests in direct numerical simulation of homogeneous isotropic turbulence [da Silva and Pereira, Phys. Fluids 19, 035106 (2007)] and in spatially evolving turbulent plane jets [da Silva and Métais, J. Fluid Mech. 473, 103 (2002)], as well as a posteriori (large eddy simulation) tests in a round jet are carried out and show that the present viscous structure function model improves the results from the classical approaches and at a comparatively small computational cost.