Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-29T08:51:21.066Z Has data issue: false hasContentIssue false

The reflection of short gravity waves on a non-uniform current

Published online by Cambridge University Press:  24 October 2008

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

Abstract

A uniform asymptotic solution is obtained which describes the propagation near an isolated caustic of water waves on a slow irrotational current. Unlike earlier work there is no restriction to straight caustics or to steady currents.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Gargett, A. E. and Hugnes, B. A.On the interaction of surface and internal waves. J. Fluid Mech. 52 (1972), 179191.CrossRefGoogle Scholar
(2)Garrett, C. J. R.Discussion: the adiabatic invariant for wave propagation in a non-moving medium. Proc. Roy. Soc. Ser. A 299 (1967), 2627.Google Scholar
(3)Hector, D., Cohen, J. and Bleistein, N.Ray method expansions for surface and interna waves in inhomogeneous oceans of variable depth. Stud. Appl. Math. 51 (1972), 121137.CrossRefGoogle Scholar
(4)Keller, J. B.Surface waves on water of non-uniform depth. J. Fluid Mech. 4 (1958), 607614.CrossRefGoogle Scholar
(5)Longuet-Higgins, M. S. and Stewart, R. W.Changes in the form of short gravity waves on long waves and tidal currents. J. Fluid Mech. 8 (1960), 565583.CrossRefGoogle Scholar
(6)Longuet-Higgins, M. S. and Stewart, R. W.The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10 (1961), 529549.CrossRefGoogle Scholar
(7)Longuet-Higgins, M. S. and Stewart, R. W.Radiation stresses in water waves; a physical discussion, with applications. Deep-Sea Rea. 11 (1964), 529562.Google Scholar
(8)Ludwig, D.Uniform asymptotic expansions at a caustic. Comm. Pure Appl. Math. 19 (1966), 215250.CrossRefGoogle Scholar
(9)McKee, W. D.Waves on a shearing current: a uniformly valid asymptotic solution. Proc. Cambridge Philos. Soc. 75 (1974), 295302.CrossRefGoogle Scholar
(10)Peregrine, D. H.River currents and trains of waves. Bull. Inst. Math. Applics. 8 (1972), 326328.Google Scholar
(11)Peregrine, D. H. and Smith, R.Stationary gravity waves on non-uniform free streams: Jet like streams. Math. Proc. Cambridge Philos. Soc. 77 (1975), 415438.CrossRefGoogle Scholar
(12)Smith, R.Edge waves on a beach of mild slope. Q. Jl Mech. Appl. Math. 27 (1974), 101110.CrossRefGoogle Scholar
(13)Stoker, J. J.Water waves (Interscience, New York, 1957).Google Scholar
(14)Taylor, G. I.The action of a surface current used as a breakwater. Proc. Roy. Soc. Ser A 231 (1955), 466478.Google Scholar