Abstract
A statistical theory for compressible turbulent shear flows subject to buoyancy effects is developed. Important correlation functions in compressible shear flows are calculated with the aid of a multiscale direct‐interaction approximation. They are expressed in the gradient‐diffusion form similar to the eddy‐viscosity representation for the Reynolds stress in incompressible flows. The results obtained are applicable to subgrid modeling, and a Smagorinsky‐type model in compressible flows is constructed.