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Gravity waves on water of variable depth

Published online by Cambridge University Press:  28 March 2006

George F. Carrier
George F. Carrier
Affiliation:
Harvard University, Cambridge, Mass.
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Abstract

This is a study of the propagation of gravity waves over a basin in which the propagation distance is large compared with the scale of the bottom topography, which, in turn, is large compared with the depth. Special emphasis is given to the low-frequency part of the spectrum and to geometries containing a beach (see figure 1) because of their importance in tidal wave phenomena. Both reflexion phenomena and the dispersive character of the propagation are accounted for and the non-linear aspects of the large amplification associated with the beach climbing are also included. However, the analysis of problems in which the waves break is valid only up to the inception of breaking; post-breaking phenomena are not treated.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 4 , April 1966, pp. 641 - 659
Copyright
© 1966 Cambridge University Press

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References

Carrier, G. F. & Greenspan, H. P. 1958 Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4, 97.Google Scholar
Chester, C., Friedman, B. & Ursell, F. 1957 An extension of the method of steepest descents. Proc. Camb. Phil. Soc. 58, 599.Google Scholar
Kajiura, K. 1961 On the partial reflection of water waves passing over a bottom of variable depth. I.U.G.G. Monograph, 24.Google Scholar
Kajiura, K. 1963 The leading wave of a Tsunami. Bull. Earthquake Res. Aust. 41, 535.Google Scholar
Mahony, J. J. 1962 An expansion method for singular perturbation problems. J. Aust. Math. Soc. 2, 440.Google Scholar
Stoker, J. J. 1948 The formation of breakers and bores. Comm. Pure Appl. Math. 1, 1.Google Scholar