Accurate series solutions for gravity-driven Stokes waves

Dallaston, Michael C. & McCue, Scott W. (2010) Accurate series solutions for gravity-driven Stokes waves. Physics of Fluids, 22(082104).

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In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

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6 citations in Scopus
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5 citations in Web of Science®

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ID Code: 33174
Item Type: Journal Article
Refereed: Yes
Additional URLs:
DOI: 10.1063/1.3480394
ISSN: 1070-6631
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2010 American Institute of Physics
Copyright Statement: Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics
The following article appeared in (Physics of Fluids, v22, 8, 2010) and may be found at
Deposited On: 19 Jul 2010 21:59
Last Modified: 29 Feb 2012 14:20

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