Dispersion relations for periodic water waves with surface tension and discontinuous vorticity

Calin Iulian Martin

doi:10.3934/dcds.2014.34.3109

Article Contents

2014, Volume 34, Issue 8: 3109-3123. Doi: 10.3934/dcds.2014.34.3109

This issue Previous Article Particle trajectories in extreme Stokes waves over infinite depth Next Article A characterization of the symmetric steady water waves in terms of the underlying flow

Dispersion relations for periodic water waves with surface tension and discontinuous vorticity

Calin Iulian Martin^1,

1.
Institut für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien

Received: August 2013

Revised: September 2013

Published: August 2014

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Abstract

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 vorticity adjacent to the free surface and is irrotational below.

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Mathematics Subject Classification: Primary: 35Q31, 35Q35, 76D33, 76D45; Secondary: 12D10.

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