Hostname: page-component-7c8c6479df-27gpq Total loading time: 0 Render date: 2024-03-28T12:26:20.939Z Has data issue: false hasContentIssue false

Dynamics of crescent water wave patterns

Published online by Cambridge University Press:  04 August 2005

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

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
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)