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Local Bifurcation for Steady Periodic Capillary Water Waves with Constant Vorticity

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Abstract

We study periodic capillary waves at the free surface of water in a flow with constant vorticity over a flat bed. Using bifurcation theory the local existence of waves of small amplitude is proved even in the presence of stagnation points in the flow. We also derive the dispersion relation.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090, Vienna, Austria

    Calin Iulian Martin

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  1. Calin Iulian Martin
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Correspondence to Calin Iulian Martin.

Additional information

Communicated by A. Constantin

C.I. Martin acknowledges the support of the ERC Advanced Grant “Nonlinear Studies of Water Flows with Vorticity”.

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Martin, C.I. Local Bifurcation for Steady Periodic Capillary Water Waves with Constant Vorticity. J. Math. Fluid Mech. 15, 155–170 (2013). https://doi.org/10.1007/s00021-012-0096-z

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  • DOI: https://doi.org/10.1007/s00021-012-0096-z

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