The effect of spanwise wall oscillation on spatially developing compressible transitional boundary layers

Spanwise wall oscillation is an easily implemented active control scheme. It can delay the transition to turbulent flows in incompressible boundary layers under appropriate control parameters. However, this delayed transition in compressible boundary layers has not yet been confirmed numerically. In this paper, we perform a series of direct numerical simulations of a spatially developing subsonic boundary layer with different spanwise wall oscillation periods and amplitudes. We numerically confirm the delay in the transition under appropriate control parameters. The delayed transition can be explained by the Stokes boundary layer induced by the spanwise wall oscillation affecting the streamwise vortices. The superposed spanwise velocity and streamwise vorticity observed in the Stokes boundary layer can weaken the development of instability in the original streamwise vortices under appropriate control parameters, leading to a delayed transition. Furthermore, the spanwise wall oscillation changes the flow compressibility, as can be inferred from the equation for the velocity divergence. The enhanced compressibility around the pre-transition regions also stabilizes the development of the streamwise vortices and causes a delayed transition.