Stability of a supersonic near-wall flow over a shallow grooved plate in the freestream of Mach 6 is investigated by means of numerical simulations and wind-tunnel experiments. Numerical solutions of two-dimensional Navier-Stokes equations are used to model propagation of artificial disturbances of several fixed frequencies generated by an actuator placed on the wall. It is shown that the high-frequency forcing excites unstable waves in the flat-plate boundary layer. These waves are relevant to the second-mode instability. The wavy wall damps the disturbances in a high-frequency band while it enhances them at lower frequencies. Stability experiments are conducted in the Institute of Theoretical and Applied Mechanics Tranzit-M shock tunnel under natural freestream conditions. The measured disturbance spectra are similar to those predicted numerically. They contain a peak associated with the second-mode instability. This peak is damped by the wavy wall, while a marginal increase of the disturbance amplitude is observed at lower frequencies. Although the experiments qualitatively confirm the wavy-wall stabilization concept, further stability and transition measurements are needed to clarify its robustness.

Numerical modeling of the time-dependent supersonic flow over a compression corner with different roundness radii is performed on the basis of the solution of the two-dimensional Navier-Stokes equations in the regimes corresponding to local boundary layer separation. The development of unstable disturbances generated by local periodic injection/suction in the preseparated boundary layer is calculated. The results are compared with those of similar calculations for a flat plate. It is shown that the natural oscillations of the boundary-layer second mode stabilize in the separation zone and grow intensely downstream of the reattachment point. The acoustic modes excited within a separation bubble are studied using numerical calculations and an asymptotic analysis.

Direct numerical simulations of a three-dimensional wave packet propagating over a 5.5 deg compression corner at the freestream Mach number 5.373 are carried out. The Navier-Stokes equations are integrated using an implicit finite volume shock-capturing method with the second-order approximation in space and time. After computing the laminar flowfield, unsteady disturbances are imposed onto the steady solution via local suction blowing on the wall surface. The undisturbed boundary layer separates upstream of the corner and reattaches downstream, forming a shallow separation bubble. The suction-blowing pulse generates a three-dimensional wave packet propagating downstream. If the pulse is produced near the leading edge, the wave packet is dominated by oblique waves relevant to the first mode, whereas plane waves of the second mode are relatively small. At sufficiently strong forcing, the nonlinear effects destabilize the wave packet in the separation region and lead to its nonlinear breakdown downstream of the reattachment line. Ultimately, a young turbulent spot is formed in the reattached boundary layer. If the pulse is produced sufficiently far downstream of the leading edge, so that the major portion of the first-mode instability region is not involved, the wave packet is dominated by the second mode. These examples show that the wave-packet contents and its downstream evolution strongly depend on how and where the initial disturbance is excited.

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