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June  2010, 13(4): 729-738. doi: 10.3934/dcdsb.2010.13.729

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

Philippe Bonneton 1, , Nicolas Bruneau 1, , Bruno Castelle 1, and  Fabien Marche 2,

1. 

Université Bordeaux 1, CNRS, UMR 5805-EPOC, avenue des Facultés, Talence, F-33405, France, France, France
2. 

Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugene Bataillon, 34095 Montpellier cedex 5, France

Received  April 2009 Revised  May 2009 Published  March 2010

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: Saint Venant equations., Shock, Wave-induced current, Vorticity, Surf zone, Rip current, Shallow water.
Mathematics Subject Classification: 74J15, 74J40, 76B15, 760.
Citation: Philippe Bonneton, Nicolas Bruneau, Bruno Castelle, Fabien Marche. Large-scale vorticity generation due to dissipating waves in the surf zone. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 729-738. doi: 10.3934/dcdsb.2010.13.729
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