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Variations on Fourier wave theory
Author(s) -
Sobey Rodney J.
Publication year - 1989
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650091203
Subject(s) - truncation (statistics) , limit (mathematics) , fourier transform , rogue wave , truncation error , mathematics , flexibility (engineering) , stokes wave , fourier analysis , fourier series , calculus (dental) , mathematical analysis , wave propagation , physics , breaking wave , optics , statistics , medicine , dentistry , nonlinear system , quantum mechanics
A review of the analytical and numerical background of Fourier wave theory establishes the commonality of existing formulations and identifies a number of analytical and numerical assumptions that are unnecessary. Some formulations in particular lack flexibility in excluding the possibility of Stokes' second definition of phase speed. A generalized formulation is introduced for comparative purposes and it is shown that published solutions differ only in the approach to the limit wave. Detailed consideration of truncation order confirms that it is the crucial parameter, especially at extreme wave heights. All formulations considered are shown to provide acceptable solutions for small to moderately extreme waves.