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A doubly localized equilibrium solution of plane Couette flow

Published online by Cambridge University Press:  05 June 2014

E. Brand  and
J. F. Gibson
E. Brand
Affiliation:
Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA
J. F. Gibson*
Affiliation:
Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized, chaotically wandering edge states of plane Couette flow. A linear analysis of dominant terms in the Navier–Stokes equations shows how the exponential decay rate and the wall-normal overhang profile of the streamwise tails are governed by the Reynolds number and the dominant spanwise wavenumber. Perturbations of the solution along its leading eigenfunctions cause rapid disruption of the interior roll-streak structure and formation of a turbulent spot, whose growth or decay depends on the Reynolds number and the choice of perturbation.

JFM classification

Instability: Instability Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 750 , 10 July 2014 , R3
Copyright
© 2014 Cambridge University Press 

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