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Climb of a bore on a beach Part 3. Run-up

Published online by Cambridge University Press:  28 March 2006

M. C. Shen  and
R. E. Meyer
M. C. Shen
Affiliation:
Brown University, Providence, Rhode Island
R. E. Meyer
Affiliation:
Brown University, Providence, Rhode Island
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Abstract

When a bore travels shoreward into water at rest on a beach, then according to the first-order non-linear long-wave theory, the bore accelerates and decreases in height, until it collapses at the shore. The investigation here reported concerns the question, what happens next? It is formulated as a singular characteristic boundary-value problem with somewhat unusual mathematical properties. Its asymptotic solution predicts a rather thin sheet of run-up and back-wash with some unexpected features.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 16 , Issue 1 , May 1963 , pp. 113 - 125
Copyright
© 1963 Cambridge University Press

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References

Barnes, E. W. 1908 Proc. Lond. Math. Soc. (2) 6, 158.
Carrier, G. F. & Greenspan, H. P. 1958 J. Fluid Mech. 4, 97.
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics, Vol. 2. New York: Interscience.
Ho, D. V. & Meyer, R. E. 1962 J. Fluid Mech. 14, 305.
Meyer, R. E. 1949 Phil. Trans. A, 242, 153.
Meyer, R. E. 1960 Theory of Characteristics of Inviscid Gas Dynamics, Encycl. of Physics, 9. Heidelberg: Springer.
Shen, M. C. & Meyer, R. E. 1963 J. Fluid Mech. 16, 108.
Stoker, J. J. 1957 Water Waves. New York: Interscience.
Whittaker, E. T. & Watson, G. N. 1940 Modern Analysis. Cambridge University Press.