Optimal disturbances in a cooled-wall hypersonic boundary layer using the One-Way Navier-Stokes (OWNS) Equations*

The dominant instability observed in adiabatic-wall flat-plate hypersonic boundary layers is the second Mack mode, which manifests itself as trapped acoustic waves between the wall and the relative sonic line. If the wall is highly cooled, not only is this mode destabilized, but an additional mode may emerge – the supersonic mode, which is characterized by an acoustic emission from the boundary layer. Accurate prediction of this mode via LST or PSE is challenging due to their underlying assumptions whereas DNS and global methods are computationally expensive. To overcome this, we instead use the One-Way Navier-Stokes (OWNS) Equations, which efficiently approximates a rigorous parabolization of the equations of motion by removing disturbances with upstream group velocity using a higher-order recursive filter. By using this method in an input/output optimization framework, we will investigate the mechanistic shift from subsonic to supersonic second mode of a Mach-6 flat-plate boundary layer by parametrically varying the wall temperature and frequency. We aim to characterize optimal disturbances under different cost functions, spatial support, and physical nature of the external disturbances.