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Dynamics of crescent water wave patterns

Published online by Cambridge University Press:  04 August 2005

D. FRUCTUS ,
C. KHARIF ,
M. FRANCIUS ,
Ø. KRISTIANSEN ,
D. CLAMOND  and
J. GRUE
D. FRUCTUS
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo. P.O. Box 1053 Blindern, 0316 Oslo, Norway
C. KHARIF
Affiliation:
Institut de Recherche sur les Phénomènes Hors-Equilibre, Technopôle de Château-Gombert, 49 Rue Frédéric Joliot-Curie, B.P. 146, 13384 Marseille Cedex 13, France
M. FRANCIUS
Affiliation:
Institut de Recherche sur les Phénomènes Hors-Equilibre, Technopôle de Château-Gombert, 49 Rue Frédéric Joliot-Curie, B.P. 146, 13384 Marseille Cedex 13, France
Ø. KRISTIANSEN
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo. P.O. Box 1053 Blindern, 0316 Oslo, Norway
D. CLAMOND
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo. P.O. Box 1053 Blindern, 0316 Oslo, Norway
J. GRUE
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo. P.O. Box 1053 Blindern, 0316 Oslo, Norway
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Abstract

The nonlinear dynamics of three-dimensional instabilities of uniform gravity-wave trains evolving to crescent wave patterns is investigated numerically. A new mechanism of generation of oscillating horseshoe patterns is proposed and a detailed discussion on their occurrence in a water wave tank is given. It is suggested that these patterns are more likely to be observed naturally in water of finite depth. A critical wave steepness for the onset of three-dimensional wave breaking due to the nonlinear evolution of quintet resonant interactions corresponding to the phase-locked crescent-shaped structures (class II instability) is provided when the quartet resonant interaction (class I instability) is absent. The nonlinear coupling between quartet resonant interactions (class I instability) and quintet resonant interactions (class II instability) leading to three-dimensional breaking waves, as shown experimentally by Su & Green (1984, 1985), is numerically investigated.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 537 , 25 August 2005 , pp. 155 - 186
Copyright
© 2005 Cambridge University Press

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