Streak growth in high-speed boundary layers: assessment through the compressible boundary region equations

Streamwise vortices and the associated streaks evolve in boundary layer flows over flat or concave surfaces as a result of various disturbances initiated in the upstream or from the wall surface. Following the transient growth, they can lead to secondary instabilities and early transition to turbulence via bursting processes. It is desirable, therefore, to accurately predict and efficiently control the growth of these disturbances in an attempt to reduce the associated frictional drag. In high-speed boundary layers, additional complications are involved due to the compressibility and thermal effects, the level of contribution of which scales with the Mach number. In this work, we study streaks in high-speed boundary layers via the numerical solution to the full nonlinear compressible boundary region equations, which is the high Reynolds number asymptotic extension of the Navier-Stokes equations in the assumption that the streamwise wavenumber of the disturbances is much smaller than the wall- normal and spanwise wavenumbers (this is characteristic to boundary layer streaks). The base flow is excited by freestream disturbances imposed at the upstream boundary, and the growth of the streaks is studied using bi-global stability analysis.