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A Lagrangian solution for internal waves

Published online by Cambridge University Press:  20 April 2006

Brian Sanderson
Brian Sanderson
Affiliation:
Department of Oceanography, University of British Columbia, 6270 University Blvd, Vancouver, B.C., Canada V6T 1W5
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Abstract

A perturbation procedure is used to obtain first- and second-order solutions for small-amplitude internal waves in a Lagrangian coordinate system. The first-order Lagrangian equations are formally accurate to the same order as the first-order Eulerian equations; however, they are different and the Lagrangian solution gives a more realistic wave shape. First-order Lagrangian solutions for internal waves in uniformly stratified fluid have a shape similar to that found in the second-order Eulerian solution. Wave profiles in uniformly stratified fluid exhibit broad crests and narrow troughs near the surface, a sinusoidal shape at mid-depth, and narrow crests and broad troughs near the bottom. The difference between the shape of crests and troughs grows as the wave amplitude is increased. Solutions obtained in a uniformly stratified fluid with a small bottom slope yield plausible shapes for breaking waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 191 - 202
Copyright
© 1985 Cambridge University Press

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