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The surface signature of internal waves

Published online by Cambridge University Press:  31 August 2012

W. Craig ,
P. Guyenne  and
C. Sulem
W. Craig*
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada
P. Guyenne
Affiliation:
Department of Mathematical Sciences, University of Delaware, DE 19716, USA
C. Sulem
Affiliation:
Department of Mathematics, University of Toronto, ON, M5S 3G3, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Oceans that are stratified by density into distinct layers support internal waves. An internal soliton gives rise to characteristic features on the surface, a signature of its presence, in the form of a ‘rip’ region, as reported in Osborne & Burch (Science, vol. 208, 1980, pp. 451–460), which results in a change in reflectance as seen in NASA photographs from the space shuttle. In the present paper, we give a new analysis of this signature of an internal soliton, and the ‘mill pond’ effect of an almost completely calm sea after its passage. Our analysis models the resonant interaction of nonlinear internal waves with the surface modes, where the surface signature is generated by a process analogous to radiative absorption. These theoretical results are illustrated with numerical simulations that take oceanic parameters into account.

JFM classification

Mathematical Foundations: Hamiltonian theory Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 710 , 10 November 2012 , pp. 277 - 303
Copyright
Copyright © Cambridge University Press 2012

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