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Higher-order resonant instabilities of internal gravity waves

Published online by Cambridge University Press:  26 April 2006

L. J. Sonmor  and
G. P. Klaassen
L. J. Sonmor
Affiliation:
Institute of Space and Atmospheric Studies, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E2 Present address: Department of Earth and Atmospheric Sciences, York University, North York, Ontario, Canada.
G. P. Klaassen
Affiliation:
Department of Earth and Atmospheric Science, York University, North York, Ontario, Canada M3J 1P3
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Abstract

We investigate the three-dimensional characteristics of a general class of resonant temporal instabilities of internal gravity waves, in which the disturbance comprises two infinitesimal internal gravity waves satisfying the conditions $\omega_I + \omega_{II} = n\tilde{\omega}$, with growth rates of order $(\vert \tilde{u}\vert \vert \tilde{k}\vert /N)^n$, assuming small dimensional primary-wave velocity amplitude $\vert \tilde{u} \vert$. We derive simple equations for their wave-numbers, frequency, growth rate, and energy budget. Interactions involving more than two disturbance components are shown not to represent distinct families of solutions, but rather to comprise order transitions linking together two or more ‘two-disturbance-component’ solutions of different order n. Unlike n = 1 resonant instabilities, those with n [ges ] 3 can align with the wave shear flow. We calculate the peak growth rate, spanwise wavenumber, and energy budget of shear-aligned resonance, as functions of wave frequency; they extract energy from both the wave shear and buoyancy fields.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 324 , 10 October 1996 , pp. 1 - 23
Copyright
© 1996 Cambridge University Press

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