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The role of transverse secondary instabilities in the evolution of free shear layers

Published online by Cambridge University Press:  26 April 2006

G. P. Klaassen  and
W. R. Peltier
G. P. Klaassen
Affiliation:
Department of Earth and Atmospheric Science, York University, North York, Ontario, Canada M3J 1P3
W. R. Peltier
Affiliation:
Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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Abstract

Linear stability analyses and nonlinear flow simulations reveal several important features of transverse secondary instabilities of two-dimensional Kelvin–Helmholtz billows and Stuart vortices. Vortex pairing is found to be the most rapidly amplified mode in a continuous spectrum of vortex merging instabilities. In certain not uncommon circumstances it is possible for more than two vortices to amalgamate in a single interaction, demonstrating that the phenomenon that has become known as the pairing resonance in fact has a rather low quality factor. Another form of merging instability in which a vortex is deformed and drained by its neighbours has been revealed by our linear stability analyses of nonlinear shear-layer disturbances. It appears, however, that this vortex draining instability may be important only in unstratified or very weakly stratified flows, since in moderately stratified Kelvin–Helmholtz flow, it is replaced by a highly localized instability which leads to a temporary distortion of the braids. Nonlinear simulations of vortex merging events in moderately stratified, high-Reynolds-number shear layers are compared to the theoretical predictions of our stability analyses. We investigate and quantify the sensitivity of merging events to variations in the initial conditions. The character of the flow after merging instability saturates and the nonlinear aspects of multiple merging events are also considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 367 - 402
Copyright
© 1989 Cambridge University Press

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