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June  2010, 13(4): 773-782. doi: 10.3934/dcdsb.2010.13.773

Focusing wave group in shallow water in the presence of wind

Julien Chambarel 1, , Christian Kharif 1, and  Olivier Kimmoun 1,

1. 

Institut de Recherche sur les Phénomènes Hors Equilibre, Technopôle de Château-Gombert 49, rue Joliot Curie - B.P. 146, 13384 Marseille Cedex 13, France, France, France

Received  March 2009 Revised  July 2009 Published  March 2010

The influence of wind on extreme wave events in shallow water is investigated numerically. A series of numerical simulations using a pressure distribution over the steep crests given by the modified Jeffreys' sheltering theory shows that wind blowing over a strongly modulated wave group due to the dispersive focusing of a chirped long wave packet increases the time duration and maximal amplitude of the extreme wave event. These results are coherent with those obtained within the framework of deep water. However, steep wave events are less unstable to wind perturbation in shallow water than in deep water.
Keywords: wind., shallow water, steep wave group.
Mathematics Subject Classification: 76B07, 76B15, 76B25, 76D33, 76M2.
Citation: Julien Chambarel, Christian Kharif, Olivier Kimmoun. Focusing wave group in shallow water in the presence of wind. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 773-782. doi: 10.3934/dcdsb.2010.13.773
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