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Climb of a bore on a beach. Part 1. Uniform beach slope

Published online by Cambridge University Press:  28 March 2006

D. V. Ho  and
R. E. Meyer
D. V. Ho
Affiliation:
Brown University, Providence, Rhode Island
R. E. Meyer
Affiliation:
Brown University, Providence, Rhode Island
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Abstract

The shoreward travel of a bore into water at rest on a beach of uniform slope is studied to elucidate why, in a class of problems—mainly gas-dynamical ones involving non-uniform shock propagation—similarity solutions seem to act like magnets attracting other solutions. For the shallow-water problem, the real magnet is shown to be the shore singularity of the governing differential equations. The shore singularity of the solution is shown to be a directional singularity of the water acceleration, for a fairly wide range of conditions, and a rather detailed asymptotic approximation for the bore development near shore is deduced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 2 , October 1962 , pp. 305 - 318
Copyright
© 1962 Cambridge University Press

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References

Carrier, G. F. & Greenspan, H. P. 1958 J. Fluid Mech. 4, 97.
Friedrichs, K. O. 1954 General Theory of High Speed Aerodynamics. Princeton University Press.
Guderley, H. 1942 Luftfahrtforschung, 19, 302.
Ho, D. V. & Meyer, R. E. 1962 Brown University Tech. Rep. no. 47, Nonr 562(07).
Keller, H. B., Levine, D. A. & Whitham, G. B. 1960 J. Fluid Mech. 7, 302.
Mahony, J. J. 1956 Phil. Trans. A, 248, 499.
Meyer, R. E. 1949 Phil. Trans. A, 242, 153.
Meyer, R. E. 1958 J. Appl. Math. Phys. (ZAMP), 9, 454.
Payne, R. B. 1957 J. Fluid Mech. 2, 185.
Stoker, J. J. 1957 Water Waves. New York: Interscience.
Whitham, G. B. 1958 J. Fluid Mech. 4, 337.