Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-24T08:28:17.331Z Has data issue: false hasContentIssue false
  • English
  • Français

On a series expansion for the solitary wave

Published online by Cambridge University Press:  21 April 2006

Stephen A. Pennell
Stephen A. Pennell
Affiliation:
Department of Mathematics, University of Lowell, Lowell, MA 01854, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The first 27 terms in a series expansion for the profile of a solitary wave are computed. From this, series expansions for the wave amplitude, mass and potential energy are obtained. A previous study indicated that the partial sums of these series converged for small- to medium-amplitude waves and that the diagonal Padé approximants converged for waves of all amplitudes. The data derived here show that this is not the case and that apparent convergence of Padé approximants can be misleading.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 557 - 561
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hunter, J. K. & Vanden-Broeck, J.-M. 1983 Accurate computations for steep solitary waves. J. Fluid Mech. 136, 63.Google Scholar
Lenau, C. W. 1966 The solitary wave of maximum amplitude. J. Fluid Mech. 26, 309.Google Scholar
Longuet-Higgins, M. S. & Fenton, J. D. 1974 On the mass, momentum, energy and circulation of a solitary wave. II. Proc. R. Soc. Lond. A 340, 471.Google Scholar
Pennell, S. A. & Su, C. H. 1984 A seventeenth-order series expansion for the solitary wave. J. Fluid Mech. 149, 431.Google Scholar
Starr, V. T. 1947 Momentum and energy integrals for gravity waves of finite height. J. Mar. Res. 6, 175.Google Scholar
Williams, J. M. 1981 Limiting gravity waves in water of finite depth. Phil. Trans. R. Soc. Lond. A 302, 139.Google Scholar
Witting, J. 1981 High solitary waves in water: results of calculations. NRL Rep. 8505.Google Scholar