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

Philippe Bonneton; Nicolas Bruneau; Bruno Castelle; Fabien Marche

doi:10.3934/dcdsb.2010.13.729

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2010, Volume 13, Issue 4: 729-738. Doi: 10.3934/dcdsb.2010.13.729

This issue Previous Article Foreword Next Article David L. Russell and a survey of his mathematical work

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

1.
Université Bordeaux 1, CNRS, UMR 5805-EPOC, avenue des Facultés, Talence, F-33405
2.
Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugene Bataillon, 34095 Montpellier cedex 5

Received: April 2009

Revised: May 2009

Published: June 2010

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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.

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Mathematics Subject Classification: 74J15, 74J40, 76B15, 7605.

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