Auto-oscillations in supersonic boundary layer

Abstract

The production of periodic oscillations in a supersonic boundary layer at the moderate and high Mach numbers (M = 2 and 5.35) is investigated within the framework of the weakly nonlinear stability theory of the second order in nonlinearity. The model includes the effects of self-action, such as the generation of stationary secondary harmonics and the disturbances of double frequencies. It is shown that for two-dimensional vortex disturbances, the character of the excitation of vortex disturbances changes from the mild one to the stiff one with the increasing Mach number, which leads to a reduction of the critical Reynolds number Re_c. For three-dimensional disturbances of low azimuthal wave numbers, a supercritical auto-oscillatory regime sets in. A complex regime realizes for two-dimensional acoustic disturbances at M = 5.35 with a stiff excitation in the region of Re_c.