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Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures

Published online by Cambridge University Press:  16 August 2010

PHILIP HALL  and
SPENCER SHERWIN
PHILIP HALL*
Affiliation:
Institute of Mathematical Sciences, Imperial College London, London SW7 2AZ, UK
SPENCER SHERWIN
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The relationship between asymptotic descriptions of vortex–wave interactions and more recent work on ‘exact coherent structures’ is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called ‘lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex–wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier–Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex–wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.

JFM classification

Flow Control: Control theory Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 661 , 25 October 2010 , pp. 178 - 205
Copyright
Copyright © Cambridge University Press 2010

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References

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