A semi-analytic solution for nonlinear standing waves in deep water
- 1 June 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 107 (-1), 147-171
- https://doi.org/10.1017/s0022112081001717
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.Keywords
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