Wavelet-based resolvent analysis for statistically-stationary and temporally-evolving flows
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.
Cite
@article{arxiv.2212.02660,
title = {Wavelet-based resolvent analysis for statistically-stationary and temporally-evolving flows},
author = {Eric Ballouz and Barbara Lopez-Doriga and Scott T. M. Dawson and H. Jane Bae},
journal= {arXiv preprint arXiv:2212.02660},
year = {2022}
}