On the Fourier approximation method for steady water waves

Zhao, Hongjun, Song, Zhiyao, Li, Ling and Kong, Jun (2014) On the Fourier approximation method for steady water waves. Acta Oceanologica Sinica, 33 5: 37-47. doi:10.1007/s13131-014-0470-1

Author Zhao, Hongjun
Song, Zhiyao
Li, Ling
Kong, Jun
Title On the Fourier approximation method for steady water waves
Journal name Acta Oceanologica Sinica   Check publisher's open access policy
ISSN 0253-505X
Publication date 2014-03-29
Year available 2014
Sub-type Article (original research)
DOI 10.1007/s13131-014-0470-1
Open Access Status
Volume 33
Issue 5
Start page 37
End page 47
Total pages 11
Place of publication Heidelberg, Germany
Publisher Springer
Collection year 2015
Language eng
Subject 1104 Complementary and Alternative Medicine
1910 Oceanography
Abstract A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximating the free surface and potential function. A set of nonlinear algebraic equations for the Fourier coefficients are derived from the free surface kinetic and dynamic boundary conditions. These algebraic equations are numerically solved through Newton's iterative method, and the iterative stability is further improved by a relaxation technology. The integral properties of steady water waves are numerically analyzed, showing that (1) the set-up and the set-down are both non-monotonic quantities with the wave steepness, and (2) the Fourier spectrum of the free surface is broader than that of the potential function. The latter further leads us to explore a modification for the present method by approximating the free surface and potential function through different Fourier series, with the truncation of the former higher than that of the latter. Numerical tests show that this modification is effective, and can notably reduce the errors of the free surface boundary conditions.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2015 Collection
School of Engineering Publications
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