Identification of Cross-Frequency Interactions in a Laminar Cavity Flow using Harmonic Resolvent Analysis*

The classical resolvent analysis identifies the input-output dynamics of fluid flow perturbations developing around a time-invariant base flow. The harmonic resolvent analysis (HRA) is an extended framework that can model time-variant and periodic base flows. For unsteady flows, HRA can elucidate the cross-frequency interactions among perturbations associated with different frequencies in the proximity of the base states. The model is built on the compressible Navier-Stokes equations, and it has been validated through an analysis of a low-Mach number flow past an airfoil compared to the incompressible case in the literature. The present work uses the HRA to analyze nonlinear perturbation dynamics in high-speed cavity flows at a Mach number of 0.8 and Reynolds number of 1500 based on the cavity depth, and the flow exhibits periodicities with multiple resonances. We reveal the optimal forcing and response modes at a coupled set of temporal frequencies and a prescribed spanwise wavenumber. The nonlinear amplification mechanism uncovered from the present work complements the extensive linear analysis of the cavity flow, providing insight into the nature of cross-frequency interactions and energy transfer mechanisms in the flow.