Study of Discrete Modes Branching in High-Speed Boundary Layers

The branching of discrete modes in high-speed boundary layers is investigated using parabolized stability equations. The fast and slow discrete modes associated with the fast and slow acoustic modes, respectively, are considered in high-speed boundary layers over adiabatic and cooled walls. Whereas the conventional linear stability theory approach leads to singular behavior in the vicinity of the fast-mode synchronization with the entropy and vorticity modes, the parabolized stability equation results do not reveal singular behavior of the solution and are consistent with the available direct numerical simulations of perturbations in high-speed boundary layers. Also, the parabolized stability equation results do not reveal a singular behavior in the vicinity of the point of synchronism of the slow and fast discrete modes.