Unsteadiness in shock-wave/boundary layer interactions

The need for better understanding of the low-frequency unsteadiness observed in shockwave/turbulent boundary layer interactions has been driving research in this area forseveral decades. This work investigates the interaction between an impinging obliqueshock and a supersonic turbulent boundary layer via large-eddy simulations. Specialcare is taken at the inlet in order to avoid introducing artificial low-frequency modesthat could affect the interaction. All simulations cover extensive integration times toallow for a spectral analysis at the low frequencies of interest. The simulations bringclear evidence of the existence of broadband and energetically-significant low-frequencyoscillations in the vicinity of the reflected shock, thus confirming earlier experimentalfindings. Furthermore, these oscillations are found to persist even if the upstreamboundary layer is deprived of long coherent structures.Starting from an exact form of the momentum integral equation and guided by datafrom large-eddy simulations, a stochastic ordinary differential equation for the reflectedshockfoot low-frequency motions is derived. This model is applied to a wide rangeof input parameters. It is found that while the mean boundary-layer properties areimportant in controlling the interaction size, they do not contribute significantly tothe dynamics. Moreover, the frequency of the most energetic fluctuations is shown tobe a robust feature, in agreement with earlier experimental observations. Under someassumptions, the coupling between the shock and the boundary layer is mathematicallyequivalent to a first-order low-pass filter. Therefore, it is argued that the observed lowfrequencyunsteadiness is not necessarily a property of the forcing, either from upstreamor downstream of the shock, but simply an intrinsic property of the coupled dynamicalsystem