Coexistence of different mechanisms underlying the dynamics of supersonic turbulent flow over a compression ramp

Supersonic turbulent flow over a compression ramp is studied using wall-resolved large eddy simulation with a freestream Mach number of 2.95 and a Reynolds number [based on delta (0): the thickness of incoming turbulent boundary layer (TBL)] of 63560. The unsteady dynamics of the present shock wave/turbulent boundary layer interaction (STBLI) flow are investigated by using dynamic mode decomposition techniques, linear and nonlinear disambiguation optimization, local stability analysis (LSA), and global stability analysis (GSA). By analyzing the dynamic system for the STBLI flow, three dynamically important modes with characteristic spanwise wavelengths of 2 delta (0), 3 delta (0), and 6 delta (0) are captured. The 2 delta (0) mode approximates the spanwise scale of the Gortler-like vortices and Gortler mode of LSA, suggesting the presence of Gortler instability, which is believed to be related to the unsteady motion of streaks downstream of reattachment in the flow. The features of the 3 delta (0) mode are also observed in large-scale motions of the incoming TBL, implying the existence of a convective mechanism that is excited and maintained by such motions. Additionally, the GSA results show the most unstable mode features a spanwise wavelength of around 6 delta (0), indicating the existence of global instability that is believed to be related to the oscillating motion of separation shock. The coexistence of these three mechanisms is confirmed. Discussions on the above findings provide an interpretation for low-frequency unsteadiness that the unsteadiness of surface streaks results from the combined effects of the Gortler instability near flow reattachment and the convection of large-scale motions in the incoming boundary layer, while the low-frequency shock motion may be related to a global mode driven by upstream disturbances.