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The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 1 Shear aligned convection, pairing, and braid instabilities

Published online by Cambridge University Press:  29 August 2012

A. Mashayek  and
W. R. Peltier
A. Mashayek*
Affiliation:
Department of Physics, University of Toronto, Ontario, M5S 1A7, Canada
W. R. Peltier
Affiliation:
Department of Physics, University of Toronto, Ontario, M5S 1A7, Canada
*
†Email address for correspondence: [email protected]
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Abstract

We study the competition between various secondary instabilities that co-exist in a preturbulent stratified parallel flow subject to Kelvin–Helmholtz instability. In particular, we investigate whether a secondary braid instability might emerge prior to the overturning of the statically unstable regions that develop in the cores of the primary Kelvin–Helmholtz billows. We identify two groups of instabilities on the braid. One group is a shear instability which extracts its energy from the background shear and is suppressed by the straining contribution of the background flow. The other group, which seems to have no precedent in the literature, includes phase-locked modes which grow at the stagnation point on the braid and are almost entirely driven by the straining contributions of the background flow. For the latter group, the braid shear has a negative influence on the growth rate. Our analysis demonstrates that the probability of finite-amplitude growth of both braid instabilities is enhanced with increasing Reynolds number and Richardson number. We also show that the possibility of emergence of braid instabilities decreases with the Prandtl number for the shear modes and increases for the stagnation point instabilities. Through detailed non-separable linear stability analysis, we show that both braid instabilities are fundamentally three dimensional with the shear modes being of small wavenumbers and the stagnation point modes dominating at large wavenumber.

JFM classification

Turbulent Flows: Shear layer turbulence Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 708 , 10 October 2012 , pp. 5 - 44
Copyright
Copyright © Cambridge University Press 2012

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A. Mashayek and W. R. Peltier

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