Study of the discrete spectrum in a mach 4.5 görtler flow

Evolution of the discrete spectrum in the M a = 4.5 boundary layer is studied with LST and PSE approaches. Both two-dimensional (2-D) and three-dimensional (3-D) disturbances are considered with streamwise curvature effects. The concave curvature shows a destabilizing effect on the 2-D second/third mode when the fast mode (mode F⁽¹⁾, mode F⁽²⁾.) synchronizes with the slow mode (mode S). The spectrum branching in the synchronization between the mode F⁽²⁾ and mode S is also observed. The increase in the spanwise wavenumber(3-D disturbances), on the other hand, suppresses the synchronization between mode F and mode S and reduces the growth rate of the unstable mode. With regard to the 3-D disturbances subjecting to the concave curvature, the mode S originating from the slow acoustic wave amounts to the unsteady Görtler mode while the quasi-steady Görtler mode emanates from the continuous spectrum of the vorticity/entropy wave.