Wall heat transfer effects on Klebanoff modes and Tollmien-Schlichting waves in a compressible boundary layer

The influence of wall heat transfer on fluctuations generated by free-stream vortical disturbances in a compressible laminar boundary layer is investigated. These disturbances are thermal Klebanoff modes, namely low-frequency, streamwise-elongated laminar streaks of velocity and temperature, and oblique Tollmien-Schlichting waves, induced by a leading-edge adjustment receptivity mechanism. The flow is governed by the linearized unsteady boundary-region equations, which properly account for the nonparallel and spanwise diffusion effects, and for the continuous forcing of the free-stream convected gusts. Wall cooling stabilizes the laminar streaks when their spanwise wavelength is much larger than the boundary-layer thickness. For these conditions, the disturbances confine themselves in the outer edge layer further downstream, where the compressibility effects are marginal. Klebanoff modes for which the spanwise diffusion is comparable with the wall-normal diffusion possess an asymptotic solution similar to the incompressible case, and are stabilized by wall heating. The unstable waves, which appear in high-Mach-number subsonic and supersonic conditions, are stabilized by wall cooling and destabilized by wall heating. Removing heat from the surface significantly shifts downstream the starting location of instability, while the streamwise wavelength and the growth rate are less affected by the wall heat flux. Perturbation methods, such as the WKBJ technique and the triple-deck theory, are used effectively to validate the numerical results and to explain the flow physics.