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Run-up and backwash bore formation from dam-break flow on an inclined plane

Published online by Cambridge University Press:  02 December 2009

MATTEO ANTUONO  and
ANDREW J. HOGG
MATTEO ANTUONO
Affiliation:
INSEAN (The Italian Ship Model Basin), US3, Via di Vallerano 139, 00128 Rome, Italy
ANDREW J. HOGG*
Affiliation:
Centre for Environmental and Geophysical Flows, School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Email address for correspondence: a.j.hogg@bris.ac.uk
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Abstract

Nonlinear shallow water equations are employed to model the inviscid slumping of fluid along an inclined plane and analytical solutions for the motion are derived using the hodograph transformation to reveal the run-up and the inception of a bore on the backwash. Starting from rest, the fluid slumps along the inclined plane, attaining a maximum run-up, before receding and forming a relatively thin and fast moving backwash. This interacts with the less rapidly moving fluid within the interior to form a bore. The evolution of the bore and the velocity and height fields either side of it are also calculated to reveal that it initially grows in magnitude before diminishing and intersecting with the shoreline. This analytical solution reveals features of the solution, such as the onset of the bore and its growth and decline, previously known only through numerical computation and the method presented here may be applied quite widely to the run-up of other initial distributions of fluid.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 640 , 10 December 2009 , pp. 151 - 164
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Antuono, M., Hogg, A. J. & Brocchini, M. 2009 The early stages of shallow flows in an inclined flume. J. Fluid Mech. 633, 285–309.CrossRefGoogle Scholar
Brocchini, M. & Baldock, T. E. 2008 Recent advances in modelling swash zone dynamics: influence of surf-swash interaction on nearshore hydrodynamics and morphodynamics. Rev. Geophys. 46 (RG3003), 1–21.CrossRefGoogle Scholar
Brocchini, M. & Dodd, N. 2008 Nonlinear shallow water equation modelling for coastal engineering. J. Waterway Port Coast. Ocean Engng 134, 104–120.CrossRefGoogle 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, 321–331.CrossRefGoogle Scholar
Hibberd, S. & Peregrine, D. H. 1979 Surf and run-up on a beach: a uniform bore. J. Fluid Mech. 95, 323–345.CrossRefGoogle Scholar
Hogg, A. J. 2006 Lock-release gravity currents and dam-break flows. J. Fluid Mech. 569, 61–87.CrossRefGoogle Scholar
Hogg, A. J. & Pritchard, D. 2004 The effects of drag on dam-break and other shallow inertial flows. J. Fluid Mech. 501, 179–212.CrossRefGoogle Scholar
Kerswell, R. R. 2005 Dam break with Coulomb friction: a model for granular slumping? Phys. Fluids 17 057101(1–16).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.), ch. 3, pp. 95–121. Academic Press.CrossRefGoogle Scholar
Peregrine, D. H. & Williams, S. M. 2001 Swash overtopping a truncated plane beach. J. Fluid Mech. 440, 391–399.CrossRefGoogle Scholar
Pritchard, D., Guard, P. A. & Baldock, T. E. 2008 An analytical model for bore-driven run-up. J. Fluid Mech. 610, 183–193.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, 1–23.CrossRefGoogle Scholar
Ritter, A. 1892 Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure 36 (33), 947–954.Google Scholar
Shen, M. C. & Meyer, R. E. 1963 Climb of a bore on a beach. Part 3. Run-up. J. Fluid Mech. 16, 113–125.CrossRefGoogle Scholar
Zhang, Q. & Liu, P. L.-F. 2008 A numerical study of swash flows generated by bores. Coast. Engng 55, 1113–1134, doi:10.1016/j.coastaleng.2008.04.010.CrossRefGoogle Scholar