Spontaneous radiation of sound by instability of a highly cooled hypersonic boundary layer

Abstract

The linear stability analysis predicts that the Mack second mode propagating in the boundary layer on a sufficiently cold plate can radiate acoustic waves into the outer inviscid flow. This effect, which is called as a spontaneous radiation (or emission) of sound, is associated with synchronization of the second mode with slow acoustic waves of the continuous spectrum. The theoretical predictions are confirmed by direct numerical simulations of wave trains and wave packets propagating in the boundary layer on a flat plate at free-stream Mach number 6 and wall-to-edge temperature ratio $T_{w}/T_{e}=0.5$. A non-uniform distribution of the wave packet components and the interference between the radiated acoustic waves result in an intricate pattern of the outer acoustic field. The spontaneous radiation of sound, in turn, strongly affects the wave packet in the boundary layer causing its elongation and modulation. This phenomenon may alter the downstream development of instability and delay the transition onset.