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A turbulent bore on a beach

Published online by Cambridge University Press:  20 April 2006

I. A. Svendsen  and
P. A. Madsen
I. A. Svendsen
Affiliation:
Institute of Hydrodynamics and Hydraulic Engineering (ISVA), Technical University of Denmark, Building 115, DK-2800, Lyngby
P. A. Madsen
Affiliation:
Institute of Hydrodynamics and Hydraulic Engineering (ISVA), Technical University of Denmark, Building 115, DK-2800, Lyngby Present address: Danish Hydraulic Institute, Hørsholm DK-2970, Denmark.
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Abstract

A theoretical model is developed giving a moderately detailed description of the flow in a turbulent bore, the velocity profiles, the shear stresses, the energy dissipation, etc. An analysis of the flow conditions at the toe of the turbulent front indicates significant differences from the usual description based on the finite-amplitude shallow-water equations, and it is shown that the present model gives a closer description of the actual physical conditions. Finally, numerical results are presented that illustrate how the model works, and test its validity on an example with known properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 148 , November 1984 , pp. 73 - 96
Copyright
© 1984 Cambridge University Press

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References

Benjamin, T. B. & Lighthill, M. J. 1954 On cnoidal waves and bores. Proc. R. Soc. Lond. A 224, 448–460.Google Scholar
Bürger, W. 1967 A note on the breaking of waves on non-uniformly sloping beaches. J. Math. & Mech. 16, 10.Google Scholar
Hibberd, S. 1977 Surf and run-up. Ph.D. thesis, University of Bristol.
Hibberd, S. & Peregrine, D. H. 1979 Surf and run-up on a beach: a uniform bore. J. Fluid Mech. 95, 323–345.Google Scholar
Hinze, J. O. 1959 Turbulence. McGraw-Hill (2nd edn 1975).
Jeffrey, A. 1964 The breaking of waves on a sloping beach. Z. angew. Math. Phys. 15, 97–106.Google Scholar
Jeffrey, A. & Mvungi, J. 1980 On the breaking of water waves in a channel of arbitrarily varying depth and width. Z. angew. Math. Phys. 31, 758–761.Google Scholar
Keller, H. B., Levine, D. A. & Whitham, G. B. 1960 Motion of a bore over a sloping beach. J. Fluid Mech. 7, 302–316.Google Scholar
Launder, B. E. & Spalding, D. B. 1972 Mathematical Models of Turbulence. Academic.
Lax, P. D. & Wendroff, B. 1960 Systems of conservation laws. Commun. Pure Appl. Maths 13, 217–237.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
Longuet-Higgins, M. S. 1973 A model of flow separation at a free surface. J. Fluid Mech. 57, 129–148.Google Scholar
Madsen, P. A. & Svendsen, I. A. 1983 Turbulent bores and hydraulic jumps. J. Fluid Mech. 129, 1–25.Google Scholar
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. Academic.
Packwood, A. R. 1980 Surf and run-up on beaches. 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 Rep. AM-81-07.Google Scholar
Peregrine, D. H. 1966 Development of an undular bore. J. Fluid Mech. 25, 321–330.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). Academic.
Peregrine, D. H. & Svendsen, I. A. 1978 Spilling breakers, bores and hydraulic jumps. In Proc. 16th Coastal Engng Conf., Hamburg, vol. I, pp. 540–550.
Richtmyer, R. D. & Morton, K. W. 1967 Difference Methods for Initial-Value Problems. Interscience.
Shen, M. C. & Meyer, R. E. 1963 Climb of a bore on a beach. Part 2. Non-uniform beach slope. J. Fluid Mech. 16, 108–112.Google Scholar
Stive, M. J. F. & Wind, H. G. 1982 A study of radiation stress and set up in the near-shore region. Coastal Engng 6, 1–26.Google Scholar
Svendsen, I. A., Madsen, P. A. & Buhr Hansen, J. 1978 Wave characteristics in the surf zone. In Proc. 16th Coastal Engng Conf., Hamburg, vol. I, pp. 520–539.
Whitham, G. B. 1958 On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4, 337–360.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Wilkinson, D. L. & Banner, M. L. 1977 Undular bores. In Proc. 6th Australasian Hydraul. and Fluid Mech. Conf., Adelaide, pp. 369–373.