Deep-water waves with vorticity: symmetry and rotational behaviour

Mats Ehrnström

doi:10.3934/dcds.2007.19.483

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2007, Volume 19, Issue 3: 483-491. Doi: 10.3934/dcds.2007.19.483

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Deep-water waves with vorticity: symmetry and rotational behaviour

Mats Ehrnström^1,

1.
Centre for Mathematical Sciences, Lund University, PO Box 118, 221 00 Lund

Received: May 2007

Revised: July 2007

Published: September 2007

Abstract / Introduction Related Papers Cited by

Abstract

We show that for steady, periodic, and rotational gravity deep-water waves, a monotone surface profile between troughs and crests implies symmetry. It is observed that if the vorticity function has a bounded derivative, then it vanishes as one approaches great depths.

Keywords:

Symmetry,
water waves,
vorticity,
nonlinear partial differential equation.

Mathematics Subject Classification: Primary: 76B15, 35Q36; Secondary: 35J25, 35J60, 76B47.

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