Growth of reattachment streaks in hypersonic compression-ramp flow

Both experiments and direct numerical simulation (DNS) of hypersonic flow over a compression ramp show streamwise aligned streaks/vortices near the corner as the ramp angle is increased. The origin of this three-dimensional disturbance growth is not definitively known in the existing literature, but is typically connected to flow deceleration, centrifugal (Görtler) and/or baroclinic effects. In this work we consider the hypersonic problem with moderate wall cooling in the high Reynolds/Mach number, weak interaction limit. In the lower deck of the corresponding asymptotic triple-deck description we pose the linearised, three-dimensional, Görtler stability equations. This formulation allows computation of both receptivity and biglobal stability problems for linear spanwise-periodic disturbances with a spanwise wavelength of the same order as the lower-deck depth. In this framework the dominant response near the ramp surface is of constant density and temperature (at leading order) ruling out baroclinic mechanisms. Nevertheless, we show that there remains strong energy growth of upstream spanwise-varying perturbations and ultimately a bifurcation from two-dimensional to three-dimensional ramp flow. The unstable eigenmodes are localised to the separation region. The bifurcation points are obtained over a range of ramp angle, wall-cooling parameter and disturbance wavelength. Consistent with DNS results, the three-dimensional perturbations in this asymptotic formulation are streamwise aligned streaks/vortices, displaced above the separation region. In addition, the growth of upstream disturbances peaks near to the reattachment point, whilst the streaks persist beyond it, decaying relatively slowly downstream along the deflected ramp.