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Two-dimensional periodic permanent waves in shallow water

Published online by Cambridge University Press:  20 April 2006

P. J. Bryant
P. J. Bryant
Affiliation:
Mathematics Department, University of Canterbury, Christchurch, New Zealand
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Abstract

When two periodic permanent wave trains on shallow water intersect obliquely, the regions of intersection are two-dimensional waves of permanent shape. This shape varies from a nearly linear superposition of the two wave trains at large angles of intersection between the wave normals, to a structure predominantly transverse to the direction of propagation at small angles of intersection. The latter shape is found to be governed by the two-dimensional Korteweg–de Vries (Kadomtsev–Petviashvili) equation. The two-dimensional permanent waves are stable to periodic disturbances parallel to their direction of propagation, but are unstable to certain oblique periodic disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 525 - 532
Copyright
© 1982 Cambridge University Press

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