The rapid–slow decomposition of the subgrid flux in inhomogeneous scalar turbulence

Abstract

In large eddy simulation of turbulent flow, because of the spatial filter, inhomogeneity and anisotropy affect the subgrid stress via the mean flow gradient. A method of evaluating the mean effects is to split the subgrid stress tensor into ‘rapid’ and ‘slow’ parts. This decomposition was introduced by Shao et al. (L. Shao, S. Sarkar, and C. Pantano, On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows, Phys. Fluids 11 (1999), pp. 1229–1248) and applied to a priori tests of existing subgrid models in the case of a turbulent mixing layer. In the present work, the decomposition is extended to the case of a passive scalar in inhomogeneous turbulence. The contributions of rapid and slow subgrid scalar flux, both in the equations of scalar energy and scalar flux, are analyzed. A priori numerical tests are performed in the turbulent Couette flow with a mean scalar gradient. Results are then used to evaluate the performances of different popular subgrid scalar models. It is shown that the existing models can not well simulate the slow part and need to be improved in future works.