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Published March 30, 2023 | Submitted
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Wavelet-based resolvent analysis for statistically-stationary and temporally-evolving flows


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.

Additional Information

Attribution 4.0 International (CC BY 4.0). The authors acknowledge support from the Air Force Office of Scientific Research under grant number FA9550-22-1-0109.

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Submitted - 2212.02660.pdf


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August 20, 2023
October 18, 2023