On Density and Pressure Fluctuations in Uniformly Sheared Compressible Flow

Abstract

Density fluctuations can be significant in a variety of flows such as high-speed flow of a compressible fluid, the mixing of separate constituents with different densities, reacting flow, and low-speed stratified flow. The behavior of density fluctuations in high-speed flow and their effect on the velocity is investigated here using DNS (direct numerical simulation) of compressible turbulence sustained by uniform mean shear. It is well-known [1, 2, 3] that, when convective Mach number increases, there is a large reduction in the thickness growth rate and turbulent intensities of the mixing layer. Although the shear is nonuniform in the mixing layer, a similar stabilizing effect on the turbulent kinetic energy K has been noticed in simulations [4, 5, 6] of uniformly sheared, compressible flow. We summarize the numerical procedure and our previous results [6] in section 2, investigate the evolution of thermodynamic fluctuations in section 3 and describe compressibility effects on the Reynolds stresses in section 4. The evolution in the presence of initially strong density and temperature fluctuations is discussed in section 5.