Three-Dimensional Nonlinear Dispersive Waves on Shear Flows |
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Authors: | V M Teshukov S L Gavrilyuk |
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Institution: | Lavrentyev Institute of Hydrodynamics, Novosibirsk UniversitèAix-Marseille III |
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Abstract: | The Green–Naghdi equations describing three-dimensional water waves are considered. Assuming that transverse variations of the flow occur at a much shorter lengthscale than variations along the wave propagation direction, we derive simplified asymptotic equations from the Green–Naghdi model. For steady flows, we show that the approximate model reduces to a one-dimensional Hamiltonian system along each stream line. Exact solutions describing a wide class of free-boundary flows depending on several arbitrary functions of one argument are found. The numerical results showing different patterns of steady three-dimensional waves are presented. |
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