Transition due to streamwise streaks in a supersonic flat plate boundary layer

Transition induced by stationary streaks undergoing transient growth in a supersonic flat plate boundary layer flow is studied using numerical computations. While the possibility of strong transient growth of small-amplitude stationary perturbations in supersonic boundary layer flows has been demonstrated in previous works, its relation to laminar-turbulent transition cannot be established within the framework of linear disturbances. Therefore, this paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite amplitude streaks in the downstream region, and then studies the modal instability of those streaks as a likely cause for the onset of bypass transition. The nonmodal evolution of linearly optimal stationary perturbations in a supersonic, Mach 3 flat plate boundary layer is computed via the nonlinear plane-marching parabolized stability equations (PSE) for stationary perturbations, or equivalently, the perturbation form of parabolized Navier-Stokes equations. To assess the effect of the nonlinear finite-amplitude streaks on transition, the linear form of plane-marching PSE is used to investigate the instability of the boundary layer flow modified by the spanwise periodic streaks. The onset of transition is estimated using anN-factor criterion based on modal amplification of the secondary instabilities of the streaks. In the absence of transient growth disturbances, first mode instabilities in a Mach 3, zero pressure gradient boundary layer reach N = 10 at Re-x approximate to 10(7). However, secondary instability modes of the stationary streaks undergoing transient growth are able to achieve the same N-factor at Re-x < 2 x 10(6) when the initial streak amplitude is sufficiently large. In contrast to the streak instabilities in incompressible flows, subharmonic instability modes with twice the fundamental spanwise wavelength of the streaks are found to have higher amplification ratios than the streak instabilities at fundamental wavelength. This behavior is shown to be related to the destabilizing influence of the streaks on oblique first mode disturbances, which tend to have longer spanwise wavelengths than those of the optimal stationary disturbances.