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A probabilistic protocol for the assessment of transition and control

Published online by Cambridge University Press:  18 May 2020

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]  and
Steven M. Tobias Open the ORCID record for Steven M. Tobias [Opens in a new window]
Anton Pershin*
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
Cédric Beaume
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
Steven M. Tobias
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
*
†Email address for correspondence: mmap@leeds.ac.uk
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Abstract

Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to turbulence is achieved via the broadening or narrowing of the basin of attraction of the laminar flow. In this paper, a novel methodology to assess the robustness of the laminar flow and the efficiency of control strategies is introduced. It relies on the statistical sampling of the phase-space neighbourhood around the laminar flow in order to assess the transition probability of perturbations as a function of their energy. This approach is applied to a canonical flow (plane Couette flow) and provides invaluable insight: in the presence of the chosen control, transition is significantly suppressed whereas plausible scalar indicators of the nonlinear stability of the flow, such as the edge-state energy, do not provide conclusive predictions. The methodology presented here in the context of transition to turbulence is applicable to any nonlinear system displaying finite-amplitude instability.

JFM classification

Instability: Transition to turbulence Instability: Nonlinear instability Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 895 , 25 July 2020 , A16
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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