Resolvent analysis of compressible flows over a long rectangular cavity

We perform global instability and resolvent analyses on compressible flows over a long rectangular cavity with a length-to-depth ratio of 6 at a depth-based Reynolds number of 502. The resolvent operator is constructed using the linearized Navier–Stokes equation to analyze the flow response to harmonic forcing. Subsonic and supersonic flows with freestream Mach numbers of 0.6 and 1.4 are studied, respectively. The result indicates that a significant energy amplification arises when the harmonic forcing has a particular combination of frequency and spanwise wavenumber. Later, we introduce unsteady blowing and suction along the cavity leading edge guided by the insights of the resolvent analysis. The unsteady forcing input is a function of spanwise wavenumber and frequency. The spatial structures of the response modes and energy amplifications are well revealed in the 2D controlled flowfields. Moreover, in the 3D case, a prominent decrease of pressure fluctuation is observed above the cavity due to the alleviation of the flow impingement strength on the cavity aft-wall. The current study shows that the resolvent analysis predicts the flow response to the leading edge forcing in direct numerical simulations.