Symmetric irrotational deep-water waves are traveling waves

In this paper, we show that a periodic solution to the irrotational two-dimensional deep-water wave problem with the horizontal velocity components at the surface, and wave profiles are symmetric, and periodic in the x-variable, necessarily defines a traveling wave. The proof relies on employing the...

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Bibliographic Details
Published in:Physics of fluids (1994) 2024-08, Vol.36 (8)
Main Authors: Li, Jian, Yang, Shaojie
Format: Article
Language:English
Subjects:
Depth profiling
Harmonic functions
Maximum principle
Traveling waves
Water waves
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Summary:In this paper, we show that a periodic solution to the irrotational two-dimensional deep-water wave problem with the horizontal velocity components at the surface, and wave profiles are symmetric, and periodic in the x-variable, necessarily defines a traveling wave. The proof relies on employing the Maximum principle for harmonic functions in unbounded domains and structural properties of the governing equations for nonlinear deep-water waves.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0223689