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The distortion of short internal waves produced by a long wave, with application to ocean boundary mixing

Published online by Cambridge University Press:  26 April 2006

S. A. Thorpe
S. A. Thorpe
Affiliation:
Department of Oceanography, The University, Southampton S09 5NH, UK
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Abstract

The propagation of a train of short, small-amplitude, internal waves through a long, finite-amplitude, two-dimensional, internal wave is studied. An exact solution of the equations of motion for a Boussinesq fluid of constant density gradient is used to describe the long wave, and its distortion of the density gradient as well as its velocity field are accounted for in determining the propagation characteristics of the short waves. To illustrate the magnitude of the effects on the short waves, particular numerical solutions are found for short waves generated by an idealized flow induced by a long wave adjacent to sloping, sinusoidal topography in the ocean, and the results are compared with a laboratory experiment. The theory predicts that the long wave produces considerably distortion of the short waves, changing their amplitudes, wavenumbers and propagation directions by large factors, and in a way which is generally consistent with, but not fully tested by, the observations. It is suggested that short internal waves generated by the interaction of relatively long waves with a rough sloping topography may contribute to the mixing observed near continental slopes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 395 - 415
Copyright
© 1989 Cambridge University Press

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