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Refraction of finite-amplitude water waves: deep-water waves approaching circular caustics

Published online by Cambridge University Press:  20 April 2006

D. H. Peregrine
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol
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Abstract

The ‘numerically exact’ properties of plane periodic deep-water waves are used in a slowly-varying-wave approximation for a steady axisymmetric wave field. The linear ‘ray’ theory for such a wave field corresponds to waves approaching a circular caustic. A parameter, C, characterizes each solution. If C is smaller than 20 the wave behaviour is dominated by the convergence of wave energy and waves are expected to break. Comparison with experiment for C = 0 indicates that breaking may be accurately predicted. If C is greater than 50 then the waves propagate closer to the caustic and, since it is of Peregrine & Smith's (1979) type R, it is likely that the waves do not break. These solutions show that wave action does not flow along the straight lines of the linear rays.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 63 - 74
Copyright
© 1981 Cambridge University Press

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