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

  • M. C. Shen (a1) and R. E. Meyer (a1)

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.

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Carrier, G. F. & Greenspan, H. P. 1958 J. Fluid Mech. 4, 97.

Courant, R. & Hilbert, D.1962Methods of Mathematical Physics, Vol. 2. New York: Interscience.

Ho, D. V. & Meyer, R. E. 1962 J. Fluid Mech. 14, 305.

Meyer, R. E.1949Phil. Trans. A, 242, 153.

Shen, M. C. & Meyer, R. E. 1963 J. Fluid Mech. 16, 108.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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