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Transient growth and nonlinear breakdown of wavelet-based resolvent modes in turbulent channel flow

Published online by Cambridge University Press:  30 July 2025

Eric Ballouz Open the ORCID record for Eric Ballouz [Opens in a new window] ,
Scott T.M. Dawson Open the ORCID record for Scott T.M. Dawson [Opens in a new window]  and
Hyunji Jane Bae Open the ORCID record for Hyunji Jane Bae [Opens in a new window]
Eric Ballouz*
Affiliation:
Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA
Scott T.M. Dawson
Affiliation:
Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
Hyunji Jane Bae
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
Corresponding author: Eric Ballouz, eballouz@stanford.edu
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Abstract

In this work, we study the effectiveness of the time-localised principal resolvent forcing mode at actuating the near wall cycle of turbulence. This mode is restricted to a wavelet pulse and computed from a singular value decomposition of the windowed wavelet-based resolvent operator (Ballouz et al. 2024b, J. Fluid Mech. vol. 999, A53) such that it produces the largest amplification via the linearised Navier–Stokes equations. We then inject this time-localised mode into the turbulent minimal flow unit at different intensities, and measure the deviation of the system’s response from the optimal resolvent response mode. Using the most energetic spatial wavenumbers for the minimal flow unit – i.e. constant in the streamwise direction and once-periodic in the spanwise direction – the forcing mode takes the shape of streamwise rolls and produces a response mode in the form of streamwise streaks that transiently grow and decay. Though other works such as Bae et al. (2021 J. Fluid Mech. vol. 914, A3) demonstrate the importance of principal resolvent forcing modes to buffer layer turbulence, none instantaneously track their time-dependent interaction with the turbulence, which is made possible by their formulation in a wavelet basis. For initial times and close to the wall, the turbulent minimal flow unit matches the principal response mode well, but due to nonlinear effects, the response across all forcing intensities decays prematurely with a higher forcing intensity leading to faster energy decay. Nevertheless, the principal resolvent forcing mode does lead to significant energy amplification and is more effective than a randomly generated forcing structure and the second suboptimal resolvent forcing mode at amplifying the near-wall streaks. We compute the nonlinear energy transfer to secondary modes and observe that the breakdown of the actuated mode proceeds similarly across all forcing intensities: in the near-wall region, the induced streak forks into a structure twice-periodic in the spanwise direction; in the outer region, the streak breaks up into a structure that is once-periodic in the streamwise direction. In both regions, spanwise oscillations account for the dominant share of nonlinear energy transfer.

JFM classification

Turbulent Flows: Turbulence control Turbulent Flows: Turbulence simulation

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JFM Papers
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Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A19
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© The Author(s), 2025. Published by Cambridge University Press

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