Computation of Three-dimensional Flexural-gravity Solitary Waves in Arbitrary Depth

Fully-localised solitary waves propagating on the surface of a three-dimensional ideal fluid of arbitrary depth, and bounded above by an elastic sheet that resists flexing, are computed. The cases of shallow and deep water are distinct. In shallow water, weakly nonlinear modulational analysis (see M...

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Bibliographic Details
Published in:Procedia IUTAM 2014, Vol.11, p.119-129
Main Authors: Wang, Zhan, Milewski, Paul A., Vanden-Broeck, Jean-Marc
Format: Article
Language:English
Subjects:
Flexural-Gravity Waves
Solitary Waves
Water Waves
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Summary:Fully-localised solitary waves propagating on the surface of a three-dimensional ideal fluid of arbitrary depth, and bounded above by an elastic sheet that resists flexing, are computed. The cases of shallow and deep water are distinct. In shallow water, weakly nonlinear modulational analysis (see Milewski & Wang 6) predicts waves of arbitrarily small amplitude and these are found numer- ically. In deep water, the same analysis rules out the existence of solitary waves bifurcating from linear waves, but, nevertheless, we find them at finite amplitude. This is accomplished using a continuation method following the branch from the shallow regime. All solutions are computed via a fifth-order Hamiltonian truncation of the full ideal free-boundary fluid equations. We show that this truncation is quantitatively accurate by comparisons with full potential flow in two-dimensions.
ISSN:2210-9838
2210-9838
DOI:10.1016/j.piutam.2014.01.054