Accurate calculations of Stokes water waves of large amplitude

William M Drennan, W. H. Hui, G. Tenti

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 coordinates x and y as double series in the stream function ψ and velocity potential φ appear to diverge. In contrast, it is shown that the direct formulation recently introduced by Hui and Tenti, in which y=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.

Original languageEnglish (US)
Pages (from-to)367-384
Number of pages18
JournalZAMP Zeitschrift für angewandte Mathematik und Physik
Volume43
Issue number2
DOIs
StatePublished - Mar 1992
Externally publishedYes

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water waves
Water waves
Water Waves
Stokes
supercomputers
Gravity waves
Supercomputers
deep water
gravity waves
Gravity Waves
Series Representation
Stream Function
Symbolic Computation
Supercomputer
Partial Sums
Diverge
formulations
Water
Series
Formulation

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

Cite this

Accurate calculations of Stokes water waves of large amplitude. / Drennan, William M; Hui, W. H.; Tenti, G.

In: ZAMP Zeitschrift für angewandte Mathematik und Physik, Vol. 43, No. 2, 03.1992, p. 367-384.

Research output: Contribution to journalArticle

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