Streaks in high-speed boundary layers: a view through the full nonlinear boundary-region equations

Abstract

Streamwise vortices and the associated streaks evolve in boundary layers over flat orconcave surfaces as a result of various disturbances initiated in the upstream or from the wall surface. Following the transient growth phase, the fully-developed vortex structures become susceptible to inviscid secondary instabilities resulting in early transition to turbulence via bursting processes. In the incompressible regime, a vast body of work hasbeen devoted to understand the initiation and development of these streaks, as well as the conditions under which they undergo secondary instabilities. For high-speed boundary layers, on the other hand, additional complications due to the compressibility and thermal effects arise, the level of contribution of which scales with the Mach number. In this paper, we study streaks in high-speed boundary layers via the numerical solution to the full nonlinear boundary region equations, which is the high Reynolds number asymptotic form of the Navier-Stokes equations, under the assumption that the streamwise wave numberof the disturbances is much smaller than the wave numbers associated with the crossflow directions, commensurate with long streamwise wavelength of the primary vortex disturbance. The effect of the spanwise separation of the vortices and the Mach number, which is varied between high-subsonic (M= 0.8) to low-hypersonic (M= 6) regimes, is quantified and discussed.