Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow

A comprehensive assessment is made of transient and asymptotic two-dimensional perturbation growth in compressible shear flow using unbounded constant shear and the Couette problem as examples. The unbounded shear flow example captures the essential dynamics of the rapid transient growth processes at high Mach numbers, while excitation by nonmodal mechanisms of nearly neutral modes supported by boundaries in the Couette problem is found to be important in sustaining high perturbation amplitude at long times. The optimal growth of two-dimensional perturbations in viscous high Mach number flows in both unbounded shear flow and the Couette problem is shown to greatly exceed the optimal growth obtained in incompressible flows at the same Reynolds number.