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Improved linear representation of ocean surface waves

Published online by Cambridge University Press:  26 April 2006

Dennis B. Creamer ,
Frank Henyey ,
Roy Schult  and
Jon Wright
Dennis B. Creamer
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, 7855 Fay Avenue, Suite 320, La Jolla, CA 92037, USA
Frank Henyey
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, 7855 Fay Avenue, Suite 320, La Jolla, CA 92037, USA
Roy Schult
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, 7855 Fay Avenue, Suite 320, La Jolla, CA 92037, USA
Jon Wright
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, 7855 Fay Avenue, Suite 320, La Jolla, CA 92037, USA
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Abstract

We apply the idea of choosing new variables that are nonlinear functions of the old in order to simplify calculations of irrotational, surface gravity waves. The usual variables consist of the surface elevation and the surface potential, and the transformation to the new variables is a canonical (in Hamilton's sense) one so as to maintain the Hamiltonian structure of the theory. We further consider the approximation of linear dynamics in these new variables. This approximation scheme exactly reproduces the effects of the lowest-order nonlinearities in the usual variables, does well at higher orders, and also captures important features of short waves interacting with longer waves. We provide a physical interpretation of this transformation which is correct in the one-dimensional case, and approximately so in the two-dimensional case.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 205 , August 1989 , pp. 135 - 161
Copyright
© 1989 Cambridge University Press

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