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Refraction of finite-amplitude water waves obliquely incident on a uniform beach

Published online by Cambridge University Press:  20 April 2006

S. Ryrie  and
D. H. Peregrine
S. Ryrie
Affiliation:
School of Mathematics, University of Bristol, England
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol, England
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Abstract

The behaviour of a periodic wavetrain propagating obliquely over water of slowly varying depth is studied. The depth contours are taken to be straight and parallel. The wave properties used are those of ‘numerically exact’ solutions for waves on water of uniform depth. Comparison is made with linear theory which proves to be quite accurate for predicting wave direction unless the waves are propagating in a direction within about 25° of the contours. The results give a direct indication of where waves may break, but do not include dissipation.

Examples are given which correspond to waves ‘trapped’ within a region of limited depth. They are related to edge waves and to caustics of the linear theory. The behaviour of solutions is consistent with earlier work on deep-water waves. This includes behaviour we term ‘anomalous refraction’, which is to be discussed in another paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 91 - 104
Copyright
© 1982 Cambridge University Press

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References

Christofferson, J. B. & Jonsson, I. G. 1980 A note on wave-action conservation in a dissipative current wave motion. Appl. Ocean Res. 2, 179–182.Google Scholar
Cokelet, E. D. 1977 Steep gravity waves in water of arbitrary uniform depth. Phil. Trans. R. Soc. Lond. A 286, 183–230.Google Scholar
Fenton, J. D. 1979 A high-order cnoidal wave theory. J. Fluid Mech. 94, 129–161.Google Scholar
Garrett, C. & Smith, J. 1976 On the interaction between long and short surface waves. J. Phys. Oceanog. 6, 925–930.Google Scholar
Hayes, W. D. 1970 Conservation of action and modal wave action. Proc. R. Soc. Lond. A 320, 187–208.Google Scholar
Longuet-Higgins, M. S. 1975 Integral properties of periodic gravity waves of finite amplitude. Proc. R. Soc. Lond. A 342, 157–174.Google Scholar
Longuet-Higgins, M. S. 1978 The instabilities of gravity waves of finite amplitude in deep water. II. Subharmonics. Proc. R. Soc. Lond. A 360, 489–505.Google Scholar
Longuet-Higgins, M. S. & Fenton, J. D. 1974 On the mass, momentum, energy and circulation of a solitary wave. II. Proc. R. Soc. Lond. A 340, 471–493.Google Scholar
Peregrine, D. H. 1981 Refraction of finite amplitude water waves: deep water waves approaching circular caustics. J. Fluid Mech. 109, 63–74.Google Scholar
Peregrine, D. H. & Smith, R. 1979 Nonlinear effects upon waves near caustics. Phil. Trans. R. Soc. Lond. A 292, 341–370.Google Scholar
Peregrine, D. H. & Thomas, G. P. 1979 Finite-amplitude deep-water waves on currents. Phil. Trans. R. Soc. Lond. A 292, 371–390.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. 2nd edn. Cambridge University Press.
Rienecker, M. M. & Fenton, J. D. 1981 A Fourier-approximation method for steady water waves. J. Fluid Mech. 104, 119–137.Google Scholar
Sakai, T. & Battjes, J. A. 1980 Wave shoaling calculated from Cokelet's theory. In Proc. 17th Internat. Conf. on Coastal Engng, ASCE.
Stiassnie, M. & Peregrine, D. H. 1979 On averaged equations for finite-amplitude water waves. J. Fluid Mech. 90, 401–405.Google Scholar
Stiassnie, M. & Peregrine, D. H. 1980 Shoaling of finite-amplitude surface waves on water of slowly varying depth. J. Fluid Mech. 97, 783–805.Google Scholar
Svendsen, I. A. & Staub, C. 1981 Horizontal particle velocities in long waves. J. Geophys. Res. 86, 4138–4148.Google Scholar
Whitham, G. B. 1974 Linear and Non-Linear Waves. Wiley-Interscience.