Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-28T10:50:39.945Z Has data issue: false hasContentIssue false

Overtopping a truncated planar beach

Published online by Cambridge University Press:  16 November 2010

ANDREW J. HOGG*
Affiliation:
Centre for Environmental and Geophysical Flows, School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
TOM E. BALDOCK
Affiliation:
School of Civil Engineering, University of Queensland, Brisbane, QLD 4072, Australia
DAVID PRITCHARD
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK
*
Email address for correspondence: a.j.hogg@bristol.ac.uk

Abstract

Run-up on a truncated impermeable beach is analysed theoretically and experimentally to find the volume of fluid, associated with a single wave event, that flows over the end of the beach. The theoretical calculations investigate the motion using the shallow-water equations and the fluid is allowed to flow freely over the end of the beach. Two models of wave events are considered: dam-break initial conditions, in which fluid collapses from rest to run-up and overtop the beach, and a waveform that models swash associated with the collapse of a long solitary bore. The calculations are made using quasi-analytical techniques, following the hodograph transformation of the governing equations. They yield predictions for the volume of fluid per unit width that overtops the beach, primarily as a function of the dimensionless length of the beach. These predictions are often far in excess of previous theoretical calculations. New experimental results are also reported in which the overtopping volumes due to flows initiated from dam-break conditions are studied for a range of reservoir lengths and heights and for a range of lengths and inclinations of the beach. Without the need for any empirically fitted parameters, good agreement is found between the experimental measurements and the theoretical predictions in regimes for which the effects of drag are negligible.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. & Stegun, I. 1964 A Handbook of Mathematical Functions. AMS-55. National Bureau of Standards.Google Scholar
Antuono, M. & Hogg, A. J. 2009 Run-up and backwash bore formation from dam-break flow on an inclined plane. J. Fluid Mech. 640, 151164.Google Scholar
Antuono, M., Hogg, A. J. & Brocchini, M. 2009 The early stages of shallow flows in an inclined flume. J. Fluid Mech. 633, 285309.CrossRefGoogle Scholar
Baldock, T. & Holmes, P. 1997 Swash hydrodynamics on a steep beach. In Coastal Dynamics 97, pp. 784793. ASCE.Google Scholar
Baldock, T. E., Barnes, M. P., Morrison, N., Shimamoto, T., Gray, D. & Nielsen, O. 2007 Application and testing of the ANUGA tsunami model for overtopping and sediment transport. In Coasts and Ports 2007, Melbourne, Australia.Google Scholar
Baldock, T. E., Hughes, M. G., Day, K. & Louys, J. 2005 Swash overtopping and sediment overwash on a truncated beach. Coast. Engng 52, 633645.CrossRefGoogle Scholar
Brocchini, M. & Dodd, N. 2008 Nonlinear shallow water equation modelling for coastal engineering. J. Waterway, Port, Coast. Ocean Engng 134, 104120.Google Scholar
Dodd, N. 1998 Numerical model of wave run-up, overtopping and regeneration. J. Waterway, Port, Coast. Ocean Engng 124 (2), 7381.Google Scholar
Donnelly, C., Kraus, N. & Larson, M. 2006 State of knowledge on measurement and modeling of coastal overwash. J. Coast. Res. 22, 965991.Google Scholar
Garabedian, P. R. 1986 Partial Differential Equations. Chelsea Publishing.Google Scholar
Guard, P. A. & Baldock, T. E. 2007 The influence of seaward boundary conditions on swash zone hydrodynamics. Coast. Engng 54, 321331.Google Scholar
Henderson, F. M. 1966 Open Channel Flow. Macmillan.Google Scholar
Hine, A. C. 1979 Mechanics of berm development and resulting beach. Sedimentology 26, 333351.Google Scholar
Hogg, A. J. 2006 Lock-release gravity currents and dam-break flows. J. Fluid Mech. 569, 6187.Google Scholar
Hogg, A. J. & Pritchard, D. 2004 a The effects of drag on dam-break and other shallow inertial flows. J. Fluid Mech. 501, 179212.Google Scholar
Hogg, A. J. & Pritchard, D. 2004 b The transport of sediment over a sloping breakwater. In Proceedings of the 15th Australasian Fluid Mechanics Conference (ed. Behnia, M., Lin, W. & McBain, G. D.). Paper AFMC 00054. The University of Sydney, Australia.Google Scholar
Hu, K., Mingham, C. G. & Causon, D. M. 2000 Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations. Coast. Engng 41, 433465.Google Scholar
Hubbard, M. E. & Dodd, N. 2002 A 2D numerical model of wave run-up and overtopping. Coast. Engng 47, 126.CrossRefGoogle Scholar
Hughes, M. G. 1995 Friction factors for wave uprush. J. Coast. Res. 11, 10891098.Google Scholar
Kerswell, R. R. 2005 Dam break with Coulomb friction: a model for granular slumping? Phys. Fluids 17, 057101(116).CrossRefGoogle Scholar
Kobayashi, N., Tega, Y. & Hancock, M. W. 1996 Wave reflection and overwash of dunes. J. Waterway, Port, Coast. Ocean Engng 122, 150153.Google Scholar
Lauber, G. & Hager, W. H. 1998 Experiments to dambreak wave: horizontal channel. J. Hydraul. Res. 36, 291307.Google Scholar
Miller, R. L. 1968 Experimental determination of run-up of undular and fully developed bores. J. Geophys. Res. 73, 44974510.CrossRefGoogle Scholar
Peregrine, D. H. 1972 Equations for water waves and the approximations behind them. In Waves on Beaches and Resulting Sediment Transport (ed. Meyer, R.), Chapter 3, pp. 95121. Academic Press.Google Scholar
Peregrine, D. H. & Williams, S. M. 2001 Swash overtopping a truncated plane beach. J. Fluid Mech. 440, 391399.CrossRefGoogle Scholar
Pritchard, D., Guard, P. A. & Baldock, T. E. 2008 An analytical model for bore-driven run-up. J. Fluid Mech. 610, 183193.CrossRefGoogle Scholar
Pritchard, D. & Hogg, A. J. 2005 On the transport of suspended sediment by a swash event on a plane beach. Coast. Engng 52, 123.Google Scholar
Puleo, J. A. & Holland, K. T. 2001 Estimating swash zone friction coefficients on a sandy beach. Coast. Engng 43, 2540.CrossRefGoogle Scholar
Reis, M. T., Hu, K., Hedges, T. S. & Mase, H. 2008 A comparison of empirical, semiempirical and numerical wave overtopping models. J. Coast. Res. 24, 250262. doi:10.2112/05-0592.CrossRefGoogle Scholar
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
Shiach, J. B., Mingham, C. G., Ingram, D. M. & Bruce, T. 2004 The applicability of the shallow water equations for modelling violent wave overtopping. Coast. Engng 51, 115.CrossRefGoogle Scholar
Synolakis, C. E. & Bernard, E. N. 2006 Tsunami science before and beyond Boxing Day 2004. Phil. Trans. R. Soc. A 364, 22312265.Google Scholar
Weir, F. M., Hughes, M. G. & Baldock, T. E. 2006 Beach face and berm morphodynamics fronting a coastal lagoon. Geomorphology 82, 331346.Google Scholar
Whitham, G. B. 1955 The effects of hydraulic resistance in the dambreak problem. Proc. R. Soc. Lond. 227, 399407.Google Scholar