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The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 2 The influence of stratification

Published online by Cambridge University Press:  03 September 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

The linear stability analyses described in Mashayek & Peltier (J. Fluid Mech., vol. 708, 2012, 5–44, hereafter MP1) are extended herein in an investigation of the influence of stratification on the evolution of secondary instabilities to which an evolving Kelvin–Helmholtz (KH) wave is susceptible in an initially unstable parallel stratified shear layer. We show that over a wide range of background stratification levels, the braid shear instability has a higher probability of emerging at early stages of the flow evolution while the secondary convective instability (SCI), which occurs in the eyelids of the individual Kelvin ‘cats eyes’, will remain a relevant and dominant instability at high Reynolds numbers. The evolution of both modes is greatly influenced by the background stratification. Various other three-dimensional secondary instabilities are found to exist over a wide range of stratification levels. In particular, the stagnation point instability (SPI), which was discussed in detail in MP1, may be of great potential importance providing alternate routes for transition of an initially two-dimensional KH wave into fully developed turbulence. The energetics of the secondary instabilities revealed by our simulations are analysed in detail and the preturbulent mixing properties are studied.

JFM classification

Turbulent Flows: Shear layer turbulence Turbulent Flows: Stratified turbulence Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 708 , 10 October 2012 , pp. 45 - 70
Copyright
Copyright © Cambridge University Press 2012

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