Surface-cooling effects on compressible boundary-layer instability, and on upstream influence

The influence of surface cooling on compressible boundary-layer instability is discussed theoretically for both viscous and inviscid modes, at high Reynolds numbers, with related questions on upstream influence being considered in an Appendix. The cooling enhances the surface heat transfer and velocity gradient, crating a high-heat-transfer sublayer. This has the effect of distorting and accentuating the viscous Tollmien-Schlichting modes to such an extent that their spatial growth rates becomes comparable with, and can even exceed, the growth rates of inviscid modes, including those found previously. This is for moderate cooling, and it applies at any Mach number. In addition, the moderate cooling destabilizes otherwise stable viscous or inviscid modes, in particular triggering outward-traveling waves at the edge of the boundary layer in the supersonic regime. Severe cooling is also discussed as it brings compressible dynamics directly into play within the viscous sublayer. All the new cooled modes found involve the heat-transfer sublayer quite actively, and they are often multistructured in form and may be distinct from those observed in previous computational and experimental investigations. The corresponding nonlinear processes are also pointed out with regard to transition in the cooled compressible boundary layer. Finally, comparisons with Lysenko and Maslov's (1984) experiments on surface cooling are presented.