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Vortex pairing and resonant wave interactions in a stratified free shear layer

Published online by Cambridge University Press:  21 April 2006

D. A. Collins  and
S. A. Maslowe
D. A. Collins
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, PQ, H3A 2K6, Canada Present address: Computer Modelling Group, Calgary, Alberta T2L 2A6, Canada.
S. A. Maslowe
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, PQ, H3A 2K6, Canada
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Abstract

In a previous study using finite-amplitude techniques (Maslowe 1977), a strong instability mechanism was discovered that takes effect at the Richardson numbers consistent with turbulence observations in the atmosphere and oceans. The mechanism involves second harmonic resonance of two neutral or nearly neutral modes at a Richardson number of roughly 0.22. In the present investigation, the nonlinear Boussinesq equations have been solved numerically to further explore this instability and to assess the limits of validity of the theory. Qualitative agreement between the theory and numerical simulations was satisfactory as the most significant numerical results were predicted by the theory. In particular, the wave interaction leads to impressive instabilities at Richardson numbers large enough that a single linearly unstable wave would amplify only weakly. At a Richardson number of 0.14, for example, the saturation amplitude of the long wave in the two-wave interacting case was 15 times as large as the amplitude of the linearly most unstable wave (evolving by itself) at the same Richardson number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 191 , June 1988 , pp. 465 - 480
Copyright
© 1988 Cambridge University Press

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