# American Institute of Mathematical Sciences

August  2014, 34(8): 3109-3123. doi: 10.3934/dcds.2014.34.3109

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

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

Received  August 2013 Revised  September 2013 Published  January 2014

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.
Citation: Calin Iulian Martin. Dispersion relations for periodic water waves with surface tension and discontinuous vorticity. Discrete & Continuous Dynamical Systems - A, 2014, 34 (8) : 3109-3123. doi: 10.3934/dcds.2014.34.3109
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