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

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 Sc t ≈ 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.