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Wavelet-based resolvent analysis of non-stationary flows

Published online by Cambridge University Press:  14 November 2024

Eric Ballouz Open the ORCID record for Eric Ballouz [Opens in a new window] ,
Barbara Lopez-Doriga Open the ORCID record for Barbara Lopez-Doriga [Opens in a new window] ,
Scott T.M. Dawson Open the ORCID record for Scott T.M. Dawson [Opens in a new window]  and
H. Jane Bae Open the ORCID record for H. Jane Bae [Opens in a new window]
Eric Ballouz*
Affiliation:
Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA
Barbara Lopez-Doriga
Affiliation:
Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
Scott T.M. Dawson
Affiliation:
Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
H. Jane Bae
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. Under this formulation, resolvent analysis may extend to turbulent flows with non-stationary mean states. The optimal resolvent modes are augmented with a temporal dimension and are able to encode the time-transient trajectories that are most amplified by the linearised Navier–Stokes equations. We first show that the wavelet- and Fourier-based resolvent analyses give equivalent results for statistically stationary flow by applying them to turbulent channel flow. We then use wavelet-based resolvent analysis to study the transient growth mechanism in the near-wall region of a turbulent channel flow by windowing the resolvent operator in time and frequency. The computed principal resolvent response mode, i.e. the velocity field optimally amplified by the linearised dynamics of the flow, exhibits characteristics of the Orr mechanism, which supports the claim that this mechanism is key to linear transient energy growth. We also apply this method to non-stationary parallel shear flows such as an oscillating boundary layer, and three-dimensional channel flow in which a sudden spanwise pressure gradient perturbs a fully developed turbulent channel flow. In both cases, wavelet-based resolvent analysis yields modes that are sensitive to the changing mean profile of the flow. For the oscillating boundary layer, wavelet-based resolvent analysis produces oscillating principal forcing and response modes that peak at times and wall-normal locations associated with high turbulent activity. For the turbulent channel flow under a sudden spanwise pressure gradient, the resolvent modes gradually realign themselves with the mean flow as the latter deviates. Wavelet-based resolvent analysis thus captures the changes in the transient linear growth mechanisms caused by a time-varying turbulent mean profile.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 999 , 25 November 2024 , A53
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© The Author(s), 2024. Published by Cambridge University Press

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