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Nonlinear interactions between deep-water waves and currents

Published online by Cambridge University Press:  06 December 2011

R. M. Moreira and
D. H. Peregrine
R. M. Moreira*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Present address: Computational Fluid Dynamics Laboratory, Fluminense Federal University, Rua Passo da Pátria 156, bl.D, sl.563A, Niterói, RJ 24210-240, Brazil. Email address for correspondence: roger@vm.uff.br
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Abstract

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The effects of nonlinearity on a train of linear water waves in deep water interacting with underlying currents are investigated numerically via a boundary-integral method. The current is assumed to be two-dimensional and stationary, being induced by a distribution of singularities located beneath the free surface, which impose sharp and gentle surface velocity gradients. For ‘slowly’ varying currents, the fully nonlinear results confirm that opposing currents induce wave steepening and breaking within the region where a high convergence of rays occurs. For ‘rapidly’ varying currents, wave blocking and breaking are more prominent. In this case reflection was observed when sufficiently strong adverse currents are imposed, confirming that at least part of the wave energy that builds up within the caustic can be released in the form of partial reflection and wave breaking. For bichromatic waves, the fully nonlinear results show that partial wave blocking occurs at the individual wave components in the wave groups and that waves become almost monochromatic upstream of the blocking region.

JFM classification

Waves/Free-surface Flows: Surface gravity wavesWaves/Free-surface Flows: Wave breakingWaves/Free-surface Flows: Waves/Free-surface Flows

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012, pp. 1 - 25
Copyright
Copyright © Cambridge University Press 2011

Footnotes

‡

Professor Peregrine passed away before this paper was completed. This manuscript was prepared for publication by the first author.

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