A Statistical Theory of Thermally-Driven Turbulent Shear Flows, with the Derivation of a Subgrid Model

Abstract

A statistical theory is presented for the turbulent motion of an incompressible fluid subject to the Boussinesq convection. The Reynolds stress and the heat flux for arbitrary mean velocity and temperature distributions are calculated with the aid of the two-scale Direct-Interaction formalism, i.e., the DI formalism incorporated with the separation of scales of the mean and fluctuating fields. The two quantities are expressed in terms of binary correlations and responses of the fluctuating field, and these expressions are simplified by the use of the inertial-range theory. As an application of the results, a subgrid model is derived for the large-eddy simulation of turbulent shear flows with buoyancy effects.