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Longshore motion generated on beaches by obliquely incident bores

Published online by Cambridge University Press:  20 April 2006

S. C. Ryrie
Affiliation:
School of Mathematics, University of Bristol Present address: Department of Computer Studies and Mathematics, Bristol Polytechnic.

Abstract

Numerical solutions of the two-dimensional shallow-water equations are found for motion on a sloping beach generated by a single bore and by a periodic succession of bores, both incident at small angles. For the latter, periodic longshore motion can always be found if bottom friction (described here by the Chezy law) in included. The timescale of the development of longshore motion is also considered.

Type
Research Article
Copyright
© 1983 Cambridge University Press

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References

Battjes, J. A. 1972 Set-up due to irregular waves. In Proc. 13th Intl Conf. Coastal Engng, Vancouver, pp. 19932004.
Bowen, A. J. & Guza, R. T. 1978 Edge waves and surf beat J. Geophys. Res. 83, 19131920.Google Scholar
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics, vol. II. Interscience.
Galvin, C. J. & Eagleson, P. S. 1965 Experimental studies of longshore currents on a plane beach. U.S. Army Coastal Engng Res. Center, Tech. Mem. 10.
Grant, W. D. & Madsen, O. S. 1979 Combined wave and current interaction with a rough bottom J. Geophys. Res. 84, 17971808.Google Scholar
Hibberd, S. & Peregrine, D. H. 1979 Surf and run-up on a beach: a uniform bore. J. Fluid Mech. 95, 323345.Google Scholar
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
Komar, P. D. 1976 Beach processes and sedimentation. Prentice-Hall.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Longuet-Higgins, M. S. 1970a Longshore currents generated by obliquely incident sea waves, 1 J. Geophys. Res. 75, 67786789.Google Scholar
Longuet-Higgins, M. S. 1970b Longshore currents generated by obliquely incident sea waves, 2 J. Geophys. Res. 75, 67906801.Google Scholar
Meyer, R. E. 1969 Note on wave run-up J. Geophys. Res. 75, 687690.Google Scholar
Meyer, R. E. & Taylor, A. D. 1972 Run-up on beaches. In Waves on Beaches (ed. R. E. Meyer), pp. 357411. Academic.
Packwood, A. R. 1980 Surf and run-up on a beach. Ph.D. thesis, University of Bristol.
Packwood, A. R. & Peregrine, D. H. 1981 Surf and run-up on beaches: models of viscous effects. Univ. Bristol, School of Maths, Rep. AM-81–07.Google Scholar
Peregrine, D. H. 1972 Equations for water waves and the approximations behind them. In Waves on Beaches (ed. R. E. Meyer), pp. 95121. Academic.
Richtmyer, R. D. & Morton, K. W. 1967 Difference Methods for Initial Value Problems, 2nd edn. Wiley-Interscience.
Ryrie, S. C. 1982 Waves on a beach: longshore motion due to surf beat of obliquely incident waves (unpublished manuscript).
Sampson, P. 1978 The longshore velocity of waves on sloping beaches. M.Sc. dissertation, University of Bristol.
Shen, M. C. & Meyer, R. E. 1963 Climb of a bore on a beach. Part 3. Run-up J. Fluid Mech., 16, 113125.Google Scholar
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