Stability of Compressible Boundary Layers Induced by a Moving Wave

Abstract

Summary The problem of determining the stability of compressible vis­ cous flows with nonzero surface velocities is formulated and is shown to be identical to that for conventional boundary layers, with only a redefinition of the Mach and Reynolds numbers re­ quired. Specific consideration is given to the wall boundary layer behind a moving shock wave, and the minimum critical Reynolds numbers are obtained for various shock velocities. The entire stability map is determined for the limiting case of a weak wave, which is analogous to the Rayleigh problem. The minimum critical Reynolds number is found to increase monotonically with shock velocity—i.e., with increasing surface cooling and stream Mach number combined. For the ratio of wall to stream velocity of 2.92 with y = 1.4 (shock Mach number of 2.18) the flow is found to be infinitely stable to two-dimension al disturbances. Experimental transition data do not follow the trends predicted by the theory. In fact, the transition Reynolds numbers are orders of magnitude below the computed minimum critical Reynolds numbers. The lack of correlation between theory and experiment is attributed to disturbances which are external to the boundary layer.