Wavelet-based resolvent analysis for statistically-stationary and temporally-evolving flows

TL;DR

This paper develops a wavelet-based resolvent analysis framework that extends traditional Fourier-based methods to analyze non-stationary turbulent flows, capturing transient structures and flow evolution.

Contribution

It introduces a novel wavelet-based resolvent analysis method applicable to non-stationary turbulent flows, validated against Fourier methods for stationary cases.

Findings

Wavelet-based analysis matches Fourier results for stationary flows.

Method captures transient growth in turbulent buffer layers.

Applicable to temporally-evolving shear flows and flow perturbations.

Abstract

This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. This allows resolvent analysis to be extended to turbulent flows with non-stationary means in addition to statistically-stationary flows. The optimal resolvent modes for this formulation correspond to the potentially time-transient structures that are most amplified by the linearized Navier-Stokes operator. We validate this methodology for turbulent channel flow and show that the wavelet-based and Fourier-based resolvent analyses are equivalent for statistically-stationary flows. We then apply the wavelet-based resolvent analysis to study the transient growth mechanism in the buffer layer of a turbulent channel flow by windowing the resolvent operator in time and frequency. The method is also applied to temporally-evolving parallel shear flows such as an oscillating boundary layer and three-dimensional channel flow, in which a lateral pressure gradient perturbs a fully-developed turbulent flow in a channel.