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Optimizing the control of transition to turbulence using a Bayesian method

Published online by Cambridge University Press:  27 April 2022

Anton Pershin Open the ORCID record for Anton Pershin [Opens in a new window] ,
Cédric Beaume Open the ORCID record for Cédric Beaume [Opens in a new window] ,
Tom S. Eaves Open the ORCID record for Tom S. Eaves [Opens in a new window]  and
Steven M. Tobias Open the ORCID record for Steven M. Tobias [Opens in a new window]
Anton Pershin*
Affiliation:
Department of Physics, University of Oxford, Oxford OX1 3PU, UK School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
Cédric Beaume
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
Tom S. Eaves
Affiliation:
School of Science and Engineering, University of Dundee, Dundee DD1 4HN, UK
Steven M. Tobias
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: [email protected]
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Abstract

The nonlinear robustness of laminar plane Couette flow is considered under the action of in-phase spanwise wall oscillations by computing properties of the edge of chaos, i.e. the boundary of its basins of attraction. Three measures are used to quantify the chosen control strategy on laminar-to-turbulent transition: the kinetic energy of edge states (local attractors on the edge of chaos), the form of the minimal seed (least energetic perturbation on the edge of chaos), and the laminarization probability (the probability that a random perturbation from the laminar flow of given kinetic energy will laminarize). A novel Bayesian approach is introduced to enable the accurate computation of the laminarization probability at a fraction of the cost of previous methods. While the edge state and the minimal seed provide useful information about the dynamics of transition to turbulence, neither measure is particularly useful to judge the effectiveness of the control strategy since they are not representative of the global geometry of the edge. In contrast, the laminarization probability provides global information about the edge and can be used to evaluate the control effectiveness by computing a laminarization score (the expected laminarization probability) and the associated expected dissipation rate of the controlled flow. These two quantities allow for the determination of optimal control parameter values subject to desired constraints. The results discussed in the paper are expected to be applied to a wide range of transitional flows and control strategies aimed at suppressing or triggering transition to turbulence.

JFM classification

Instability: Transition to turbulence Instability: Nonlinear instability Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A25
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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