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Giant waves

Published online by Cambridge University Press:  11 April 2006

Ronald Smith
Ronald Smith
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

It is suggested that giant waves, as observed on the Agulhas Current, occur where the wave groups are reflected by the current. The local behaviour of the wave amplitude is modelled by the nonlinear Schrodinger equation

iar = aρρ-ρ+β|a|2a.

For waves of a given incident wave amplitude the steady solutions are stable.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 3 , 8 October 1976, pp. 417 - 431
Copyright
© 1976 Cambridge University Press

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References

Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. J. Fluid Mech. 27, 417–430.Google Scholar
Bretherton, F. P. & Garrett, C. J. R. 1969 Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. A 302, 529–554.Google Scholar
Davey, A. & Stewartson, K. 1974 On three-dimensional packets of surface waves. Proc. Roy Soc. A 338, 101–110.Google Scholar
Davis, H. T. 1962 Introduction to Nonlinear Differential and Integral Equations. Dover.
Holliday, D. 1973 Nonlinear gravity-capillary surface waves in a slowly varying current. J. Fluid Mech. 57, 797–802.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1961 Changes in the form of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10, 529–549.Google Scholar
Mckee, W. D. 1974 Waves on a shearing current: a uniformly valid asymptotic solution. Proc. Camb. Phil. Soc. 75, 295–302.Google Scholar
Mallory, J. K. 1974 Abnormal waves on the south east coast of South Africa. Int. Hydrog. Rev. 51, 99–129.Google Scholar
Nayfeh, A. H. 1973 Perturbation Methods. Interscience.
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. A. Mech. 16, 9–117.Google Scholar
Peregrine, D. H. & Teomas, G. P. 1976 Finite amplitude water waves on currents. Surface Gravity Waves on Water of Varying Depth (ed. R. Radok).Google Scholar
Sanderson, R. M. 1974 The unusual waves off South East Africa. Marine Observer, 44, 180–183.Google Scholar
Smith, R. 1975 The reflection of short gravity waves on a non-uniform current. Math. Proc. Camb. Phil. Soc. 78, 517–525.Google Scholar
Sturm, H. 1974 Giant waves. Ocean, 2 (3), 98–101.Google Scholar
Writham, G. B. 1965 A general approach to linear and nonlinear waves using a Lagrangian. J. Fluid Mech. 22, 273–283.Google Scholar