The modeling of variable density turbulent flows - A review of first-order closure schemes

The paper is intended as a review of where eddy-viscosity turbulence models have reached in accounting for the several distinct effects of variable density and high-Mach number behaviour on the development of turbulent shear flows. Three generations of "compressible models'' are depicted: a first one based on variable density and compressible adjustments of "incompressible'' schemes, a second one in which it is presumed that explicit dilatational terms can account for variable density and compressibility effects, and a third one, where such effects are taken implicitly in association with structural changes of the turbulent field. The latter are hardly tractable when using first-order closure schemes, but more reliable than the former in accounting for most observed variable density and compressibility effects in turbulent shear flows.