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Surf and run-up on a beach: a uniform bore

Published online by Cambridge University Press:  19 April 2006

S. Hibberd
Affiliation:
School of Mathematics, University of Bristol Present address: Department of Theoretical Mechanics, University of Nottingham.
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol

Abstract

A numerical solution is obtained to describe the behaviour of a uniform bore over a sloping beach and the subsequent run-up and back-wash. The results exhibit features which have only previously been described in a qualitative manner. These include the formation’ of a landward-facing bore in the back-wash. A comprehensive set of results are presented for a typical initial subcritical bore height ratio.

Type
Research Article
Copyright
© 1979 Cambridge University Press

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References

Carrier, G. F. & Greenspan, H. P. 1958 Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4, 97109.Google Scholar
Coulson, C. A. & Jeffrey, A. 1977 Waves: A Mathematical Approach to the Common Types of Wave Motion (2nd edition) Longman.
Freeman, J. C. & Le Méahautéa, B. 1964 Wave breakers on a beach and surges on a dry bed. Proc. A.S.C.E., Hyd. Div. 90, 187215.Google Scholar
Friedman, M. P. 1960 Shock waves propagating through non-uniform regions. J. Fluid Mech. 8, 193209.Google Scholar
Halls, J. & Carr, A. 1975 Nearshore Sediment Dynamics and Sedimentation. Wiley.
Hibberd, S. 1979 Approximations to offshore bore travel. In preparation
Ho, D. V. & Meyer, R. E. 1962 Climb of a bore on a beach 1, Uniform beach slope. J. Fluid Mech. 14, 305318.Google Scholar
Houghton, D. D. & Kasahara, A. 1968 Non-linear shallow fluid flow over an isolated ridge. Comm. Pure Appl. Math. 21, 123.Google Scholar
Jeffrey, A. 1964 The breaking of waves on a sloping beach. Z. angew. Math. Phys. 15, 97106.Google Scholar
Kajiura, K. 1976 Local behaviour of tsunamis. Proc. IUTAM Symp. Surface Gravity Waves on Water of Variable Depth (ed. R. Radok and D. G. Provis). Canberra: Australian Academy of Science. Springer.
Keller, H. B., Levine, D. A. & Whitham, G. B. 1960 Motion of a bore over a sloping beach. J. Fluid Mech. 7, 302316.Google Scholar
Lax, P. & Wendroff, B. 1960 Systems of conservation laws. Comm. Pure Appl. Math. 13, 217237.Google Scholar
Meyer, R. E. 1972 Waves on Beaches and Resulting Sediment Transport. New York: Academic Press.
Meyer, R. E. & Taylor, A. D. 1972 Run-up on beaches. In Waves on Beaches and Resulting Sediment Transport (ed. R. E. Meyer), pp. 357–411. New York: Academic Press.
Miller, R. L. 1968 Experimental determination of run-up of undular and fully developed bores. J. Geophys. Res. 73, 44974510.Google Scholar
Peregrine, D. H. 1972 Equations for water waves and the approximations behind them. In Waves on Beaches and Resulting Sediment Transport (ed. R. E. Meyer), pp. 95–121. New York: Academic Press.
Peregrine, D. H. 1974 Water wave interaction in the surf zone. Proc. 14th Conf. Coastal Engng, pp. 500517.Google Scholar
Radok, R. & Provis, D. G. 1977 Waves on Water of Variable Depth. Lecture Notes in Physics vol. 64, Springer.
Richtmyer, R. D. & Morton, K. W. 1967 Difference Methods for Initial Value Problems (2nd edition). Wiley-Interscience.
Shen, M. C. & Meyer, R. E. 1963 Climb of a bore on a beach 3: Run-up. J. Fluid Mech. 16, 113125.Google Scholar
Sielecki, A. & Wurtele, M. G. 1970 The numerical integration of the non-linear shallow water equations with sloping boundaries. J. Comp. Phys. 6, 219236.Google Scholar
Spielvogel, L. Q. 1976 Single-wave run-up on beaches. J. Fluid Mech. 74, 685694.Google Scholar
Svendsen, I. A., Madsen, P. A. & Hansen, J. B. 1978 Wave characteristics in the surf zone. Proc. 16th Coastal Eng. Conf. Hamburg, A.S.C.E.
Whitham, G. B. 1958 On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337360.Google Scholar