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Notes on long-crested water waves

Published online by Cambridge University Press:  20 April 2006

A. J. Roberts  and
D. H. Peregrine
A. J. Roberts
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver St. Cambridge CB3 9EW Present address: Department of Applied Mathematics, University of Adelaide, GPO Box 498, Adelaide, South Australia 5001.
D. H. Peregrine
Affiliation:
School of Mathematics, University Walk, Bristol BS8 1TW
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Abstract

Fully three-dimensional surface gravity waves in deep water are investigated in the limit in which the length of the wave crests become long. We describe an analytic solution to fourth order in wave steepness, which matches onto known short-crested wave solutions on the one hand and onto the well-known two-dimensional progressivewave solution on the other. In the progressive-wave limit a particular solution in which the wave crests are semi-finite is given to sixth-order accuracy. These solutions are part of a more general set of solutions which are found from a nonlinear Schrödinger equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 323 - 335
Copyright
© 1983 Cambridge University Press

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