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Computation of Nonlinear Wave Kinematics During Propagation and Runup on a Slope

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Water Wave Kinematics

Part of the book series: NATO ASI Series ((NSSE,volume 178))

Abstract

An efficient Boundary Element Method (BEM) solving fully nonlinear waterwave problems in the physical space has been developed in our earlier papers. Its detailed numerical features have been presented elsewhere. In the present paper, this method is applied to the computation of the interaction between highly nonlinear solitary waves and plane steep and gentle slopes. Kinematics of the waves is calculated during propagation and runup on a slope. In particular, the internal velocity field above the slope and the pressure force on the slope are computed in detail during runup and rundown of the wave. The results show features of the wave flow such as jet-like up-rush, stagnation point and breaking during backwash. A comparison is made with accurate experimental results (runup, surface elevations), with orther fully nonlinear solutions, and also with the predictions of the Shallow Water Wave Equation. The results show that the BEM used here is capable of accurately describing the wave flow and interaction with a plane slope(2.88° to 90°), in great detail.

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References

  1. Brorsen, M. & Larsen, J. Source Generation of Nonlinear Gravity Waves with the Boundary Integral Method. Coastal Engineering 11, 93–113, 1987.

    Article  Google Scholar 

  2. Byatt-Smith, J.G.B. The Reflection of a Solitary Wave by a Vertical Wall. J. Fluid Mech. 197, 503–521, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  3. Camfield, F.E. & Street, R.L. An Investigation of the Deformation and Breaking of Solitary Waves. Dept. of Civil Engng. f Stanford University, Technical Report No. 81, 1967.

    Google Scholar 

  4. Carrier, G.F. Gravity Waves on Water of Variable Depth. J. Fluid Mech. 24 (4), 641–659, 1966.

    Article  MATH  MathSciNet  Google Scholar 

  5. Carrier, G.F. & Greenspan, H.P. Water Waves of Finite Amplitude on a Sloping Beach. J. Fluid Mech. 4 (1), 97–110, 1958.

    Article  MATH  MathSciNet  Google Scholar 

  6. Cointe, R., Molin, B. & Nays, P. Nonlinear and Second-Order Transient Waves in a Rectangular Tank. In Proc. 6th Intl. Conf. on Behavior of Off-shore Structures, Delft (B.O.S.S.), 1988.

    Google Scholar 

  7. Dold, J.W. & Peregrine, D.H. Steep Unsteady Water Waves: An Efficient Computational Scheme. In Proc. 19th Intl. Conf. on Coastal Engineering, Houston, USA, pp. 955–967, 1984.

    Google Scholar 

  8. Dommermuth, D.G. & Yue, D.K.P. Numerical Simulation of Nonlinear Axisymmetric Flows with a Free Surface. J. Fluid Mech. 178, 195–219, 1987.

    Article  MATH  Google Scholar 

  9. Fenton, J.D. & Rienecker, M.M. A Fourier Method for Solving Nonlinear Water-Wave Problems: Application to Solitary-Wave Interactions. J. Fluid Mech. 118, 411–443, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  10. Gardner, C.S., Greene, J.M., Kruskal, M.D. & Miura, R.M. Method for Solving the Korteweg-de Vries Equation. Physical Revue Letters 19, (19), 1095–1097, 1967.

    Article  MATH  Google Scholar 

  11. Goring D.G. Tsunamis - The Propagation of Long Waves onto a Shelf. W.M. Keck Laboratory of Hydraulics and Water Ressources, California Institute of Technology, Report No. KH-R-38, 1978.

    Google Scholar 

  12. Greenhow, M. & Lin, W.M. Numerical Simulation of Nonlinear Free Surface Flows Generated by Wedge Entry and Wave-maker Motions. In Proc. 4th Intl. Conf. on Numerical Ship Hydrody., Washington, USA, 1985.

    Google Scholar 

  13. Greenhow, M. & Lin, W.M. The Interaction of Nonlinear Free Surfaces and Bodies in Two Dimensions. MARINTEK, Report No. OR/53/530030.12/01/86, 36 pps, 1986.

    Google Scholar 

  14. Grilli, S., Skourup, J. & Svendsen, I.A. The Modelling of Highly Nonlinear Waves: A Step Toward the Numerical Wave Tank. Invited paper in Proc. 10th Intl. Conf. on Boundary Elements, Southampton, England, Vol. 1 (ed. C.A. Brebbia), pp. 549–564.

    Google Scholar 

  15. Grilli, S., Skourup, J. & Svendsen, I.A. An Efficient Boundary Element Method for Nonlinear Water Waves. Engineering Analysis with Boundary Elements 6 (2), 1989.

    Google Scholar 

  16. Grilli, S. & Svendsen, I.A. The Modelling of Highly Nonlinear Waves. Part 2: Some Improvements to the Numerical Wave Tank. To appear in Proc. 11th Intl. Conf. on Boundary Elements, Cambridge, Massachusetts, USA. Computational Mechanics Publication. Springer Verlag, Berlin, 1989a.

    Google Scholar 

  17. Grilli, S. & Svendsen, I.A. The Modelling of Nonlinear Water Wave Interaction with Maritime Structures. To appear in Proc. 11th Intl. Conf. on Boundary Elements, Cambridge f Massachusetts, USA. Computational Mechanics Publication. Springer Verlag, Berlin, 1989b.

    Google Scholar 

  18. Hall, J.V. & Watts, J.W. Laboratory Investigation of the Vertical Rise of Solitary Waves on Impermeable Slopes. Beach Erosion Board, US Army Corps of Engineer, Tech. Memo. No. 33, 14 pp, 1953.

    Google Scholar 

  19. Hammack, J.L. & Segur, H. The Korteweg-de Vries Equation and Water Waves. Part 2. Comparison with Experiments. J. Fluid Mech. 65 (2), 289–314, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  20. Kim, S.K., Liu, P.L.-F. & Liggett, J.A. Boundary integral Equation Solutions for Solitary Wave Generation Propagation and Run-up. Coastal Engineering 7, 299–317, 1983.

    Article  Google Scholar 

  21. Kravtchenko, J. Remarques sur le calcul des amplitudes de la houle lineaire engendrée par un batteur. In Proc. 5th Intl. Conf. on Coastal Engineering, pp. 50–61, 1954.

    Google Scholar 

  22. Lin, W.M., Newman, J.N. & Yue, D.K. Nonlinear Forced Motion of Floating Bodies. In Proc. 15th Intl. Symp. on Naval Hydrody., Hamburg, Germany, 1984.

    Google Scholar 

  23. Longuet-Higgins, M.S. & Cokelet, E.D. The Deformation of Steep Surface Waves on Water - I. A Numerical Method of Computation. Proc. R. Soc. Lond. A350, 1–26, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  24. Losada, M.A. Vidal, C. & Nunez, J. Sobre El Comportamiento de Ondas Propagádose por Perfiles de Playa en Barra y Diques Sumergidos.Direción General de Puertos y costas Programa de Clima Maritimo. Unibersidad de Cantábria. Publación No. 16, 1986.

    Google Scholar 

  25. Mirie R.M. & Su C.H. Collisions Between Two Solitary Waves. Part 2. A Numerical Study. J. Fluid Mech. 115, 475–492, 1982.

    Article  MATH  Google Scholar 

  26. Nagai, S. Pressures of Standing Waves on Vertical walls J. Waterways, Harbors Div. ASCE 95, 53–76, 1969.

    Google Scholar 

  27. Packwood, A.R. & Peregrine, D.H. Surf and Runup on Beaches: Models of Viscous Effects. School of Mathematics, University of Bristol, Report No. AM-81-07, 1981.

    Google Scholar 

  28. Pedersen, G. & Gjevik, B. Run-up of Solitary Waves J. Fluid Mech. 135, 283–299, 1983.

    Article  MATH  Google Scholar 

  29. Peregrine, D.H. Flow Due to a Vertical Plate Moving in a Channel. Unpublished Notes, 1972.

    Google Scholar 

  30. Roberts, A.J. Transient Free-Surface Flows Generated by a Moving Vertical Plate. Q.J. Mech. Appl. Math. 40 (1), 129–158, 1987.

    Article  MATH  Google Scholar 

  31. Su, C.H. & Gardner, C.S. Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation. J. Math. Phys. 10 536–539, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  32. Su, C.H. & Mirie, R.M. On Head-on Collisions between two Solitary Waves. J. Fluid Mech. 08 509–525, 1980.

    Article  MathSciNet  Google Scholar 

  33. Svendsen, I.A. & Grili, S. Nonlinear Waves on Slopes. To appear inJ. Coastal Res., 1989

    Google Scholar 

  34. Svendsen, I.A. & Justesen, P. Forces on Slender Cylinders from Very High and Spilling Breakers. In Proc. Symp. on Description and Modelling of Directional Seas, paper No. D-7,16 pps. Technical University of Denmark, 1984.

    Google Scholar 

  35. Synolakis, C.E. The Runup of Solitary Waves. J. Fluid Mech. 185, 523–545, 1987. [12].

    Google Scholar 

  36. Tanaka, M., Dold, J.W., Lewy, M. & Peregrine, D.H. Instability and Breaking of a Solitary Wave. J. Fluid Mech. 185, 235–248, 1987.

    Article  MATH  Google Scholar 

  37. Vinje, T. & Brevig, P. Numerical Simulation of Breaking Waves. Adv. Water Ressources 4, 77–82, 1981.

    Article  Google Scholar 

  38. Yim, B. Numerical Solution for Two-Dimensional Wedge Slamming with a Nonlinear Free surface Condition. In Proc. 4th Intl. Conf. on Numerical Ship HydrodyWashington, USA, 1985.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Ocean Engineering Program, Department of Civil Engineering, University of Delaware, Newark-DE, 19716, USA

    S. Grilli & I. A. Svendsen

Authors
  1. S. Grilli
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  2. I. A. Svendsen
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Editor information

Editors and Affiliations

  1. Norwegian Hydrotechnical Laboratory, Norwegian Institute of Technology, Trondheim, Norway

    A. Tørum

  2. Statoil, Stavanger, Norway

    O. T. Gudmestad

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© 1990 Kluwer Academic Publisher

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Grilli, S., Svendsen, I.A. (1990). Computation of Nonlinear Wave Kinematics During Propagation and Runup on a Slope. In: Tørum, A., Gudmestad, O.T. (eds) Water Wave Kinematics. NATO ASI Series, vol 178. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0531-3_24

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  • DOI: https://doi.org/10.1007/978-94-009-0531-3_24

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6725-6

  • Online ISBN: 978-94-009-0531-3

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