Rapid distortion analysis of high Mach number homogeneous shear flows: Characterization of flow-thermodynamics interaction regimes
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In high-speed shear flows the nature of flow-thermodynamics interactionsconsequently 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 as in a simple harmonic oscillator and consequently shear stresses oscillate about a near zero value. Thus production is drastically reduced leading to stabilization of perturbation kinetic energy growth rate. Further increase in acoustic frequency beyond shear magnitude leads to Regime 3. The solenoidal perturbations begin to dominate the flow statistics and the kinetic energy evolution bears much semblance to the incompressible shear flow. Overall, this work leads to improved insight into high-speed shear flow physics. 2012 American Institute of Physics.
