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Motion of a bore over a sloping beach

Published online by Cambridge University Press:  28 March 2006

H. B. Keller ,
D. A. Levine  and
G. B. Whitham
H. B. Keller
Affiliation:
Institute of Mathematical Sciences, New York University
D. A. Levine
Affiliation:
Institute of Mathematical Sciences, New York University
G. B. Whitham
Affiliation:
Institute of Mathematical Sciences, New York University
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Abstract

The results of numerical calculations are presented for the motion of a bore over a uniformly sloping beach. The shallow water equations are solved in finite difference form, and a technique is developed for fitting in the bore at each step. The results are compared with the approximate formula given by Whitham (1958) and close agreement is found. The approximate theory is considered further here; the main addition is a rigorous proof that, within the shallow water theory, the height of the bore always tends to zero at the shoreline.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 2 , February 1960 , pp. 302 - 316
Copyright
© 1960 Cambridge University Press

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References

Friedman, M. P. 1959 An improved perturbation theory for shocks propagating through non-uniform regions. (To be published.)
Lax, P. D. 1954 Commun. Pure appl Math. 7, 159–93.
Whitham, G. B. 1958 J. Fluid Mech. 4, 337–60.