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Three‐Dimensional Nonlinear Dispersive Waves on Shear Flows
Author(s) -
Teshukov V. M.,
Gavrilyuk S. L.
Publication year - 2006
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2006.00342.x
Subject(s) - nonlinear system , mathematical analysis , boundary value problem , mathematics , transverse plane , mechanics , shear flow , shear (geology) , flow (mathematics) , wave propagation , classical mechanics , physics , geology , petrology , structural engineering , quantum mechanics , engineering
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.