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The propagation of large amplitude tsunamis across a basin of changing depth Part 1.Off-shore behaviour

Published online by Cambridge University Press:  29 March 2006

E. Varley ,
R. Venkataraman  and
E. Cumberbatch
E. Varley
Affiliation:
Center for the Application of Mathematics, Lehigh University
R. Venkataraman
Affiliation:
Center for the Application of Mathematics, Lehigh University
E. Cumberbatch
Affiliation:
Department of Mathematics, Purdue University
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Abstract

A theory is presented which describes the propagation of large amplitude tsunamis across a basin of variable depth in the limit when this depth is varying slowly on a scale deiined by the wavelength. In part 1 only the off-shore behaviour is considered; in part 2 some features of the final run up are described.

The technique used is to regard the wave as a slowly modulated simple wave with a slowly changing Riemann invariant. One of the most significant results is that over distances where the effect of depth variation modulates the amplitude of the wave, but does not disperse it, the variations of the amplitudes of the flow variables, such as maximum surface elevation, can be calculated as functions of the undisturbed depth without knowing how this depth varies in distance and without knowing the wave profile. These variations are fully calculated.

The work continues the investigation on large amplitude acoustic pulses in stratified media described in an earlier paper by Varley & Cumberbatch (1970). It is a generalization of Whitham's work (1953) on the sonic boom.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 4 , 29 October 1971 , pp. 775 - 801
Copyright
© 1971 Cambridge University Press

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References

Bascom, W. 1964 Waves and Beaches: The Dynamics of the Ocean Surface. New York: Doubleday.
Carrier, G. F. 1966 J. Fluid Mech. 24, 641–659.
Lamb, H. 1945 Hydrodynamics. New York: Dover.
Seymour, B. R. & Varley, E. 1970 Proc. Roy. Soc. A 314, 387–415.
Stoker, J. J. 1957 Water Waves: The Mathematical Theory with Applications. New York: Interscience.
Varley, E. & Cumberbatch, E. 1965 J. Inst. Maths. Applies. 1, 101–112.
Varley, E. & Cumberbatch, E. 1966 J. Inst. Maths. Applics. 2, 133–143.
Varley, E. & Cumberbatch, E. 1970 J. Fluid Mech. 43, 513–537.
Whitham, G. B. 1953 Comm. Pure Appl. Math. 6, 397–414.