Interaction of supersonic boundary layer instabilities with stationary streamwise streaks

Abstract eng:
The nonlinear evolution of the linearly optimal stationary perturbations in a Mach 3 flat plate boundary layer is computed using the nonlinear, perturbation form of parabolized Navier-Stokes equations. As noted in previous works, the optimal initial disturbances correspond to steady counter-rotating streamwise vortices, which subsequently lead to the formation of streamwise-elongated structures, i.e., streaks, via a lift-up effect. To assess the effect of the finite-amplitude streaks on boundary layer instabilities, the plane-marching PSE are used to investigate the instability of the boundary layer flow modified by spanwise periodic streaks. Finite-amplitude streaks are known to stabilize Tollmien-Schlichting waves in the incompressible regime. Here, subcritical streaks are observed to destabilize first mode instabilities with two spanwise wavelengths of the streak while they stabilize those with three and four spanwise wavelengths. These results support the passive flow control strategy of using micro-vortex-generators for delaying transition due to oblique first mode instabilities in supersonic boundary layers.

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