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On wave interactions in a stratified fluid

Published online by Cambridge University Press:  28 March 2006

S. A. Thorpe
S. A. Thorpe
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University and National Institute of Oceanography, Godalming, Surrey
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Abstract

Interactions between waves in a stably stratified fluid with a free or fixed upper surface may occur at second order when the horizontal wave-numbers, ki, and frequencies, σi, of the three interacting waves satisfy the relations \[ {\bf k}_1 \pm{\bf k}_2 \pm {\bf k}_3 = 0,\quad \sigma_1 \pm \sigma_2 \pm \sigma_3 = 0. \] These relations may be satisfied in the case when two free surface waves interact with an internal wave, or in the case when all three waves are internal, provided that they do not all belong to the same mode. The theory is applied to situations which might be realized in the laboratory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 4 , April 1966 , pp. 737 - 751
Copyright
© 1966 Cambridge University Press

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