Stability analyses of secondary instability and oblique breakdown in a supersonic boundary layer under the influence of pressure gradients

Studied here is how pressure gradients affect nonlinear transition processes in a supersonic flat-plate boundary layer. Linear stability analysis suggests that a favorable pressure gradient stabilizes the first-mode disturbances significantly, whereas an adverse pressure gradient destabilizes them. Nonlinear stability analysis indicates that the three nonlinear mechanisms of fundamental resonance, subharmonic resonance, and oblique breakdown can induce transition. Oblique breakdown causes the earliest transition, and subharmonic resonance is stronger than fundamental resonance. An adverse pressure gradient significantly destabilizes the primary modes and enhances the nonlinear transition mechanisms. However, a favorable pressure gradient affects the different nonlinear transition processes differently. A weak favorable pressure gradient completely suppresses the transition in fundamental resonance but just delays it slightly in subharmonic resonance. For oblique breakdown, a weak favorable pressure gradient delays the transition significantly, with two high-speed streaks observed clearly. In all cases, a strong favorable pressure gradient leads to a fully laminar flow.