Resolvent analysis of compressible laminar and turbulent cavity flows

TL;DR

This study applies resolvent analysis to both laminar and turbulent cavity flows to uncover flow physics, response structures, and frequency-dependent amplification, offering insights for flow control strategies.

Contribution

It extends resolvent analysis to open-cavity flows at different Reynolds numbers, revealing similarities in flow structures and frequency responses between laminar and turbulent regimes.

Findings

High-frequency response dominates turbulent flow amplification.

Laminar flow is more responsive to low-frequency excitation.

Flow structures from resolvent modes resemble physical flow features.

Abstract

The present work demonstrates the use of resolvent analysis to obtain physical insights for open-cavity flows. 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, we perform resolvent analysis on both laminar and turbulent flows over a rectangular cavity with length-to-depth ratio of $L/D=6$ at a free stream Mach number of $M_\infty=0.6$ in a spanwise periodic setting. Based on the dominant instability of the base state, a discount parameter is introduced to resolvent analysis to examine the harmonic characteristics over a finite-time window. We first uncover the underlying flow physics and interpret findings 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 $Re_D = 10^4$. The features of response and forcing modes from the laminar and turbulent cavity flows are similar to the spatial structures from the laminar analysis. We further find that the large amplification of energy in flow response is associated with high frequency for turbulent flow, while the flow is more responsive to low frequency excitation in the laminar case. These findings from resolvent analysis provide valuable insights for flow control studies with regard to parameter selection and placement of actuators and sensors.