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A new type of three-dimensional deep-water wave of permanent form

Published online by Cambridge University Press:  19 April 2006

Philip G. Saffman  and
Henry C. Yuen
Philip G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, California 91125
Henry C. Yuen
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, Redondo Beach, California 90278
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Abstract

A new class of three-dimensional, deep-water gravity waves of permanent form has been found using an equation valid for weakly nonlinear waves due to Zakharov (1968). These solutions appear as bifurcations from the uniform two-dimensional wave train. The critical wave heights are given as functions of the modulation wave vector. The three-dimensional patterns may be skewed or symmetrical. An example of the skewed wave pattern is given and shown to be stable. The results become exact in the limit of very oblique modulations.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 101 , Issue 4 , 29 December 1980 , pp. 797 - 808
Copyright
© 1980 Cambridge University Press

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References

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