Accurate calculations of Stokes water waves of large amplitude

  • W. M. Drennan
  • W. H. Hui
  • G. Tenti
Original Papers

Abstract

This paper reports on a detailed study of large amplitude gravity waves of the Stokes type on deep water, in which a combination of analytical work, carried out with the help of symbolic computation, and accurate numerical work performed on a supercomputer was used. Strong numerical evidence is presented showing that the Stokes method of calculation, as well as its more recent computer extensions, are questionable for intermediate to large amplitude waves. In particular, the resulting Stokes representation of the coordinatesx andy as double series in the stream functionψ and velocity potentialφ appear to diverge. In contrast, it is shown that the direct formulation recently introduced by Hui and Tenti, in whichy=y(x, ψ), produces a series representation so well behaved that accurate results for all the wave properties can be obtained with relatively low order partial sums.

Résumé

Nous présentons une étude détaillée du problème des houles (ondes de Stokes) de grande pente dans un domaine d'eau très profond, dans laquelle nous utilisons le programme de calcul symbolique Maple ainsi que le superordinateur Cray X-MP. Les résultats numériques démontrent d'une façon concluante que la méthode de Stokes et ses généralisations modernes ne sont pas recommandables dans le cas consideré ici, parce que la double série de Stokes ne semble pas converger. Nous démontrons aussi que la théorie récemment introduite par Hui et Tenti est capable, au contraire, de produire une représentation de l'onde par une série très rapidement convergente même aux grandes pentes.

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Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • W. M. Drennan
    • 1
  • W. H. Hui
    • 1
  • G. Tenti
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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