Steep Unsteady Water Waves and Boundary Integral Methods

  • D. H. Peregrine
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


Boundary-integral methods are the preferred method for modelling steep, unsteady water waves when they arc expected to break. The jet of water that forms as a wave starts to break can be modelled. Although the boundary-integral accounts for a major part of the computational running time, I shall intro-duce it as a minor part of the unsteady wave problem. Boundary-integrals are used for solving Laplace’s equation since water-waves propagating into still water are well described by inviscid irrotational fluid flow. That is the fluid velocity can be expressed as the gradient of a potential, ⌽, satisfying Laplace’s equation.


Vortex Vorticity Sine Crest Breakwater 


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  1. 1.
    Baker, G.R., Meiron, D.I. & Orzag, A.: Generalized vortex methods for free-surface flow problems. J.Fluid Mech. 123, (1982) 477–501.MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Dold, J.W. & Peregrine, D.H.: An efficient boundary-integral method for steep unsteady crater waves. “Numerical methods for fluid dynamics II”, K.W. Morton and M.J. Baines, (1986a) 671–679, Clarendon Press, Oxford.Google Scholar
  3. 3.
    Dold, J.W. & Peregrine, D.H.: Water-wave modulation. Proc. 20th Internat. Conf. Coastal Engng. Taipei, A.S.C.E. (1986b)Google Scholar
  4. 4.
    Dommermuth, D.G. & Yue, D.K.P.: Numerical simulations of nonlinear axisymmetric flows with a free surface. J.Fluid Mech. to appear.Google Scholar
  5. 5.
    Dommermuth, D.G., Yue, D.K.P., Rapp, R.J., Chan, F.S. & Melville, W.K.: Deep-water breaking waves: a comparison between potential theory and experiments. 1987. Submitted for publication.Google Scholar
  6. 6.
    Greenhow, M.: Free-surface flows related to breaking waves: J. Fluid Mech. 134 (1983) 259–275.MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Greenhow, M.: Water entry and exit of a horizontal cylinder. Proc. 2nd Internat. Workshop on Water Waves and Floating Bodies, ed. U.V. Evans, Bristol Univ. Maths. Dept. (1987).Google Scholar
  8. 8.
    Lin, W.-M., Newman, J.N. & Yue, D.K.: Nonlinear forced motions of floating bodies. 15th Sympos. Naval Hydrodynamics, Hamburg. (1984).Google Scholar
  9. 9.
    Longuet-Iliggins, M.S.: On the forming of sharp corners at a free surface. Proc.Roy.Soc.Lond. A 371 (1980) 453–78.ADSCrossRefGoogle Scholar
  10. 10.
    Longuet-Iliggins, M.S. & Cokelet, E.D.: The deformation of steep surface waves on water. I. A numerical method of computation. Proc.Roy.Soc.Lond. A 350 (1976) 1–26CrossRefGoogle Scholar
  11. 11.
    Longuet-Iliggins, M.S. & Cokelet, E.D.: The deformation of steep surface waves on water. II. Growth of normal-mode instabilities. Proc.Roy.Soc.Lond. A 364 (1978) 1–28.ADSCrossRefGoogle Scholar
  12. 12.
    New, A.L.: On the breaking of water waves. Ph.D. dissertation, Bristol University (1983).Google Scholar
  13. 13.
    New, A.L., McIver, P. & Peregrine, D.H.: Computations of breaking waves. J. Fluid Mech. 150 (1985) 233–251.ADSMATHCrossRefGoogle Scholar
  14. 14.
    Peregrine, D.H., Cokelet, E.D. & McIver, P.: The fluid mechanics of waves approaching breaking. Proc. 17th Conf. Coastal Engng. A.S.C.E. 1 (1980) 512–528.Google Scholar
  15. 15.
    Tanaka, M., Dold, J.W., Lowy, M. & Peregrine, D.H.: Ins- tability and breaking of a solitary wave. J. Fluid Mech. to appear (1987).Google Scholar
  16. 16.
    Vinje, T. & Brevik, P.: Numerical simulation of breaking waves. Adv. Water Resources, 4 (1981) 77–82.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • D. H. Peregrine
    • 1
  1. 1.School of MathematicsUniversity of BristolBristolEngland

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