Dispersion relation for water waves with non-constant vorticity
arXiv:1201.1626 · doi:10.1016/j.euromechflu.2012.03.008
Abstract
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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