Flow-thermodynamics interactions in rapidly-sheared compressible turbulence

We investigate the behavior of flow variables, thermodynamic variables and their interaction in rapidly sheared (S) homogeneous compressible turbulence using rapid distortion theory (RDT). We subject an initially isotropic and incompressible flow field to homogeneous shear-rate of various strengths quantified by a gradient Mach number (M _g ) based on characteristic wavenumber. Our objective is to characterize the behavior of flow/thermodynamic fluctuations and their linear interactions during the course of turbulence evolution. Even though the mean shear-rate is held constant, the gradient Mach number progressively diminishes with time as the relevant wavenumber increases due to the mean deformation. The evolution exhibits three distinct phases which we categorize based on the character of pressure as: (i) Pressure-released (PR) stage which is observed when ${St < \sqrt{M_{g0}}}$ and pressure effects are negligible; (ii) Wave-character (WC) stage wherein ${\sqrt{M_{g0}} < St < M_{g0}}$ and the wave character of pressure is in evidence; and (iii) Low-Mach number (LM) stage when St > M _g0, where M _g0 is the initial gradient Mach number. In the PR regime we find that the thermodynamic fluctuations evolve from their initial state but velocity fluctuations grow unhindered by pressure fluctuations. In the WC regime, the pressure fluctuations become significant and flow-thermodynamic interaction commences. This interaction brings about equipartition of dilatational kinetic energy and thermodynamic potential energy. The interaction also results in stabilization of turbulence, and the total kinetic energy growth comes to a near standstill. Ultimately in the LM stage, kinetic energy starts increasing again with the growth rate being very similar to that in incompressible RDT. However, the thermodynamic fluctuations continue to grow despite the gradient Mach number being substantially smaller than unity. Overall, the study yields valuable insight into the linear processes in high Mach number shear flows and identifies important closure modeling issues.