Acoustic-vortical evolution mechanisms of supersonic first Mack mode

This study employs linear stability theory, direct numerical simulation, and momentum potential theory to investigate the physical characteristics of the first mode at varying spanwise wavenumbers in a Mach 4.5 flat-plate boundary layer and subsequently examines the influence of porous coatings. As the spanwise wavenumber increases, the streamwise wavenumber initially rises before declining, with its maximum marking the transition of the first mode from an acoustic to a vortical nature. Momentum potential theory is then applied to decompose fluctuating momentum in the perturbation field into vortical, acoustic, and thermal components. The results indicate that as the spanwise wavenumber increases, the proportion of acoustic components diminishes, while vortical components progressively dominate. These distinct physical characteristics lead to divergent responses to porous coatings: Slightly oblique first modes are modulated by scattering effects and wall admittance, while highly oblique first modes are destabilized by mean flow distortions induced by the coatings.