Resolvent analysis of compressible laminar and turbulent cavity flows

The present work demonstrates the use of a resolvent analysis to obtain physical insights for open-cavity flows. A resolvent analysis identifies the flow response to harmonic forcing, given a steady base state, in terms of the response and forcing modes and the amplification gain. The response and forcing modes reveal the spatial structures associated with this amplification process. In this study, a resolvent analysis is performed on both laminar and turbulent flows over a rectangular cavity with a length-to-depth ratio of L/D 6 at a freestream Mach number of M_∞ 0.6 in a spanwise periodic setting. Based on the dominant instability of the base state, a discount parameter is introduced to a resolvent analysis to examine the harmonic characteristics over a finite-time window. First, the underlying flow physics is uncovered and the findings are interpreted from laminar flow at Re_D 502. These findings from laminar flow are extended to a more practical cavity flow example at a much higher Reynolds number of Re_D 10⁴ . The features of response and forcing modes from the turbulent cavity flow are similar to the spatial structures from the laminar analysis. It is further found that the large amplification of energy in the flow response is associated with the high frequency (St_L ≳ 2.5) for turbulent flow, whereas the flow is more responsive to the low-frequency (St_L ≲ 0.4) excitation in the laminar case. These findings from the resolvent analysis provide valuable insights for flow control studies with regard to parameter selection and the placement of actuators and sensors.