Competition of the multiple Görtler modes in hypersonic boundary layer flows

Competition of multiple Görtler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode (mode W) and the trapped-layer mode (mode T) both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge. The mode T has the largest growth rate at a lower Görtler number while the mode W dominates at larger Görtler numbers. These two modes are both responsible for the flow transition in the hypersonic flows especially when Görtler number is in the high value range in which the crossover of these two modes takes place. Such high Görtler numbers are virtually far beyond the neutral regime. The nonparallel base flows, therefore, cease to influence the stability behavior of the Görtler modes. The effects of the Mach number on the multiple Görtler modes are studied within a chosen Mach number of 0.95, 2, 4 and 6. When the flow Mach number is sufficiently large, e.g., Ma 4, the growth rate crossover of the mode T and mode W occurs both in the conventional G-β map as well as on the route downstream for a fixed wavelength disturbance. Four particular regions (Region T, T-W, W-T and W) around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis. The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.