Rebecca Bertsch

Rapid distortion analysis of high Mach number homogeneous shear flows: Characterization of flow-thermodynamics interaction regimes

In high-speed shear flows the nature of flow-thermodynamics interactions, and consequently the character of transition/turbulence, changes markedly with Mach number. We identify and characterize three different regimes of interactions in terms of acoustic frequency-to-shear magnitude ratio employing the linear rapid distortion analysis. We begin with an analysis of the pressure equation and demonstrate that acoustic frequency grows monotonically with time in this initial value problem whereas the shear magnitude is imposed to be constant. Initially when acoustic frequency is smaller than shear magnitude, fluctuations grow rapidly as the velocity field evolves unrestrained by pressure. This corresponds to Regime 1 wherein there is no significant flow-thermodynamics interaction. Flow-thermodynamics interactions commence in Regime 2 as acoustic frequency grows to the level of imposed shear rate. Dilatational velocity and pressure fields in the flow-normal direction are generated. The two fields are coupled a...

Rapid distortion analysis of high speed homogeneous turbulence subject to periodic shear

The effect of unsteady shear forcing on small perturbation growth in compressible flow is investigated. In particular, flow-thermodynamic field interaction and the resulting effect on the phase-lag between applied shear and Reynolds stress are examined. Simplified linear analysis of the perturbation pressure equation reveals crucial differences between steady and unsteady shear effects. The analytical findings are validated with numerical simulations of inviscid rapid distortion theory (RDT) equations. In contrast to steadily sheared compressible flows, perturbations in the unsteady (periodic) forcing case do not experience an asymptotic growth phase. Further, the resonance growth phenomenon found in incompressible unsteady shear turbulence is absent in the compressible case. Overall, the stabilizing influence of both unsteadiness and compressibility is compounded leading to suppression of all small perturbations. The underlying mechanisms are explained.