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Improved linear representation of surface waves. Part 2. Slowly varying bottoms and currents

Published online by Cambridge University Press:  26 April 2006

Jon Wright  and
Dennis B. Creamer
Jon Wright
Affiliation:
Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0402, USA
Dennis B. Creamer
Affiliation:
Naval Research Laboratory, Washington, DC 20375-5000, USA
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Abstract

We extend the results of a previous paper to fluids of finite depth. We consider the Hamiltonian theory of waves on the free surface of an incompressible fluid, and derive the canonical transformation that eliminates the leading order of nonlinearity for finite depth. As in the previous paper we propose using the Lie transformation method since it seems to include a nearly correct implementation of short waves interacting with long waves. We show how to use the Eikonal method for slowly varying currents and/or depths in combination with the nonlinear transformation. We note that nonlinear effects are more important in water of finite depth. We note that a nonlinear action conservation law can be derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 261 , 25 February 1994 , pp. 65 - 74
Copyright
© 1994 Cambridge University Press

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