Review of linear compressible stability theory

Aspects of the linear compressible stability theory are considered, with special attention given to the inviscid theory and the additional solutions that arise when there is a region of supersonic flow relative to the phase velocity. For the case of highly cooled flat-plate boundary layers at Mach number 5.8, the unstable region is found to include supersonic outgoing waves. A previously unknown neutral incoming wave has also been identified. An example of viscous multiple solutions is provided, and calculations of higher viscous discrete modes and the compressible counterpart of the Squire mode are presented. It is noted that compressible stability theory is missing a firm connection with boundary-layer transition.