On the role of discrete and continuous modes in a cooled high-speed boundary layer flow

Abstract

The disturbance flow field for a Mach Formula Presented flat-plate boundary layer flow with a wall-to-free-stream temperature ratio of Formula Presented is studied using direct numerical simulation (DNS), linear stability theory (LST) and biorthogonal decomposition. In the second-mode instability region, the DNS flow field can be reconstructed using a single LST mode, namely Formula Presented. However, when the supersonic mode emerges, none of the discrete modes nor the continuous branches alone can precisely match the DNS data. A superposition of the pair of discrete supersonic modes Formula Presented and the slow acoustic continuous spectrum is required to reproduce the disturbance amplitude distributions and the amplification rates observed in the DNS. Another finding is that the supersonic mode Formula Presented, which should be decaying following LST, in actuality is amplified based on the projected DNS data.