Spectral perturbation theory for wall-admittance effects on compressible boundary-layer instability

Thin wall treatments modify high-speed boundary-layer instability through the pressure they admit or absorb at the wall. This paper develops a unified admittance formulation for such effects on trapped compressible Rayleigh modes. For a simple rigid-wall eigenpair, we prove the spectral sensitivity law $$c(A)=c_0+KA+\mathcal{O}(\mathrm{\mid }A{\mathrm{\mid }}^2),\delta \sigma =\alpha \text{Imag}(KA)+\mathcal{O}(\mathrm{\mid }A{\mathrm{\mid }}^2),$$ where $A$ is the wall admittance and $K$ is an explicit functional of the rigid-wall eigenfunction. The formula separates wall physics from outer-mode physics and yields a phase criterion for stabilisation. Matched asymptotics show that viscous and thermal wall layers, blind-pore coatings and shallow non-separating roughness all reduce to this same boundary condition, with additive leading admittances. Mach-4.5 computations validate the sensitivity coefficient and demonstrate porous damping, viscous-wall damping and sign-changing reactive roughness effects.