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The influence of stratification on secondary instability in 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

We analyse the stability of horizontally periodic, two-dimensional, finite-amplitude Kelvin-Helmholtz billows with respect to infinitesimal three-dimensional perturbations having the same streamwise wavelength for several different levels of the initial density stratification. A complete analysis of the energy budget for this class of secondary instabilities establishes that the contribution to their growth from shear conversion of the basic-state kinetic energy is relatively insensitive to the strength of the stratification over the range of values considered, suggesting that dynamical shear instability constitutes the basic underlying mechanism. Indeed, during the initial stages of their growth, secondary instabilities derive their energy predominantly from shear conversion. However, for initial Richardson numbers between 0.065 and 0.13, the primary source of kinetic energy for secondary instabilities at the time the parent wave climaxes is in fact the conversion of potential energy by convective overturning in the cores of the individual billows. A comparison between the secondary instability properties of unstratified Kelvin-Helmholtz billows and Stuart vortices is made, as the latter have often been assumed to provide an adequate approximation to the former. Our analyses suggest that the Stuart vortex model has several shortcomings in this regard.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 71 - 106
Copyright
© 1991 Cambridge University Press

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