Effect of wall temperature on Görtler instability-induced high-speed boundary layer transition

The effect of wall temperature on Görtler instability-induced transition for a high-speed boundary layer on a concave wall with Mach 6 is investigated systematically with direct numerical simulations and stability analyses. Three wall temperatures (Tw) are considered separately, i.e., Tw = 300 K (cooling wall), 393 K (adiabatic wall temperature), and 500 K (heating wall), corresponding to wall temperature ratios ranging from 0.76 to 1.27. The linear stability theory is employed to analyze primary instability characteristics in the undisturbed laminar boundary layer. Görtler vortices are excited by stationary blowing and suction, which induce streaky structures downstream. Increasing the wall temperature will delay the growth of the streak amplitude but increase the saturation amplitudes of the streaks. The transition process is triggered by superimposing random disturbances and can be divided into three regions featuring: initial streak oscillations, large-scale vortical structures, and small-scale turbulence proliferation, respectively. BiGlobal analysis and plane-marching parabolized stability equations (PSE3D) are adopted to identify and characterize secondary instability modes. It is demonstrated that varicose modes dominate on cooling wall, generating localized knotty structures. Increasing wall temperature suppresses secondary instabilities and changes the dominated mode type, correlating with enhanced sinuous streak oscillations and delayed breakdown observed in direct numerical simulations (DNS). The modal growth rates predicted by PSE3D align closely with DNS results in the linear stage, while diverge downstream due to nonlinear interactions.