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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Large-scale vorticity generation due to dissipating waves in the surf zone

Pages: 729 - 738, Volume 13, Issue 4, June 2010      doi:10.3934/dcdsb.2010.13.729

 
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Philippe Bonneton - Université Bordeaux 1, CNRS, UMR 5805-EPOC, avenue des Facultés, Talence, F-33405, France (email)
Nicolas Bruneau - Université Bordeaux 1, CNRS, UMR 5805-EPOC, avenue des Facultés, Talence, F-33405, France (email)
Bruno Castelle - Université Bordeaux 1, CNRS, UMR 5805-EPOC, avenue des Facultés, Talence, F-33405, France (email)
Fabien Marche - Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugene Bataillon, 34095 Montpellier cedex 5, France (email)

Abstract: In this paper, we investigate the mechanisms which control the generation of wave-induced mean current vorticity in the surf zone. From the vertically-integrated and time-averaged momentum equations given recently by Smith [21], we obtain a vorticity forcing term related to differential broken-wave energy dissipation. Then, we derive a new equation for the mean current vorticity, from the nonlinear shallow water shock-wave theory. Both approaches are consistent, under the shallow water assumption, but the later gives explicitly the generation term of vorticity, without any ad-hoc parametrization of the broken-wave energy dissipation.

Keywords:  Surf zone, Shallow water, Wave-induced current, Rip current, Vorticity, Shock, Saint Venant equations.
Mathematics Subject Classification:  74J15, 74J40, 76B15, 7605.

Received: April 2009;      Revised: May 2009;      Available Online: March 2010.