Bi-global crossplane stability analysis of high-speed boundary-layer flows with discrete roughness

Bi-global secondary linear stability theory (B-SLST) is applied to a laminar Mach 4.8 flat-plate boundary-layer flow altered by discrete roughness elements, roughly 0 5 undisturbed boundary-layer thicknesses high. The steady primary state earned by DNS with the immersed-boundary technique shows a counter-rotating vortex pair (CVP) generating a low-speed streak in the roughness' centerline wake. The resulting wall-normal and spanwise shear promotes 1st-mode instability, increasing the growth rate roughly by a factor of four. Two modes are obtained a symmetric y-mode and an antisymmetric z-mode. A comparison with an unsteady DNS, where time-periodic 2-d perturbations are introduced upstream of the roughness, shows well matching growth rates and amplitude distribution of the y-mode.