Dispersion relation for water waves with non-constant vorticity
نویسندگان
چکیده
منابع مشابه
Dispersion relation for water waves with non-constant vorticity
We derive the dispersion relation for linearized small-amplitude gravity waves for various choices of non-constant vorticity. To the best of our knowledge, this relation is only known explicitly in the case of constant vorticity. We provide a wide range of examples including polynomial, exponential, trigonometric and hyperbolic vorticity functions.
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We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.
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The influence of an underlying current on three-wave interactions of capillary water waves is studied. The fact that in irrotational flow resonant three-wave interactions are not possible can be invalidated by the presence of an underlying current of constant non-zero vorticity. We show that: 1) wave trains in flows with constant non-zero vorticity are possible only for two-dimensional flows, 2...
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We derive the dispersion relation for water waves with surface tension and having a piecewise constant vorticity distribution. More precisely, we consider here two scenarios; the first one is that of a flow with constant non-zero vorticity adjacent to the flat bed while above this layer of vorticity we assume the flow to be irrotational. The second type of flow has a layer of non-vanishing vort...
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ژورنال
عنوان ژورنال: European Journal of Mechanics - B/Fluids
سال: 2012
ISSN: 0997-7546
DOI: 10.1016/j.euromechflu.2012.03.008