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.


Solitary Wave Boundary Element Method Breaking Wave Generalize Vortex Vortex Sheet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations