Linear evolution and interaction of disturbances in the boundary layers on impermeable and porous surfaces in the presence of heat transfer

The interaction of disturbances in the compressible boundary layers on both impermeable and porous surfaces is considered in the linear and nonlinear approximations (weakly-nonlinear stability theory) in the presence of surface cooling. The regimes of moderate (Mach number M = 2) and high (M = 5.35) supersonic velocities are considered. It is established that surface cooling leads a considerable change in the linear evolution of the disturbances, namely, the first-mode vortex disturbances are stabilized, whereas the second-mode acoustic disturbances are destabilized, the variation degree being determined by the temperature factor. A porous coating used for controlling flow regimes influences the stability in the opposite fashion. For vortex waves the nonlinear interactions in three-wave systems at M = 2 are considerably attenuated in the presence of cooling. It might be expected that the cooling of the surface can delay the laminar regime for M = 2 and accelerate transition to turbulence for M = 5.35.