Instability of compressible three-dimensional boundary layers to stationary disturbances

Abstract

The stability of compressible three-dimensional boundary layers to stationary disturbances is examined on the basis of the linear stability theory. Comparisons of stability characteristics are made between the subsonic and supersonic boundary layers at the edge Mach numbers 0.2 and 2.0, respectively. The result shows that the boundary layer becomes unstable to stationary three-dimensional modes when the cross-flow velocity exceeds a rather small threshold of less than 1% of the external flow velocity. Important to note that the critical Reynolds number for stationary modes does not strongly depend on the Mach number. It is also found that the wavelength of the most amplified stationary three-dimensional mode is four or five times the boundary-layer thickness, not depending on the magnitude of cross-flow velocity both for the subsonic and supersonic flows.