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Steady deep-water waves on a linear shear current. (English) Zbl 0572.76022

The properties of steady, periodic, deep-water gravity waves on a linear shear current are investigated. Numerical solutions for all waveheights, up to and including the limiting ones, are computed from a formulation which involves only the wave profile (parametrized in a natural way) and some constants of the motion. It is found that for some shear currents the highest waves are not necessarily those waves with sharp crests known as extreme waves.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M99 Basic methods in fluid mechanics
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References:

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