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A semi-analytic solution for nonlinear standing waves in deep water

Published online by Cambridge University Press:  20 April 2006

L. W. Schwartz  and
A. K. Whitney
L. W. Schwartz
Affiliation:
Applied Mathematics Department, University of Adelaide, Adelaide, South Australia
A. K. Whitney
Affiliation:
Applied Mechanics Laboratory, Lockheed Research Laboratory, Palo Alto, California
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Abstract

A method of time-dependent conformal mapping is introduced to simplify the power-series solution procedure for time- and space-periodic standing waves in deep water. A solution has been found to 25th order in the wave amplitude. The values of certain coefficients are determined by the requirement that secular terms must be suppressed. Because the series for the wave profile is not always uniformly convergent, Padé approximants are used for summation. For very high waves, the slope of the surface has at least two relative maxima. The singularity structure of the solution is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 107 , June 1981 , pp. 147 - 171
Copyright
© 1981 Cambridge University Press

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