Instability Mechanisms in the Compressible Falkner–Skan Boundary Layers with A Cooled Wall

We study the stability of compressible Falkner Skan boundary layers over a wedge at hypersonic speeds (target location Mae = 7). For a cooled wall with temperature ratio Tratio = 0.25 (wall temperature scaled by the corresponding adiabatic value), we compute accurate basic solution via Laguerre spectral method and perform a temporal linear stability analysis to locate the critical Reynolds number Rec and streamwise wavenumber αc. A key result is quite unexpected: as the favorable pressure-gradient parameter β increases, Rec decreases (from 115.3 at β = 0 to 83.5 at β = 0.3), opposite to the classical incompressible Falkner-Skan boundary layer. In contrast, for an adiabatic wall (Tratio = 1), Rec increases with β (from 107.7 to 153.1), recovering the classical behavior. A fluid–thermodynamic energy decomposition shows that vortical contributions to the instability are predominantly stabilizing, whereas the thermal and acoustic contributions strengthen with β under cooled wall conditions, thereby lowering the stability threshold.