An exact integral equation for solitary waves (with new numerical results for some 'internal' properties)

Evans, Andy and Ford, M.J. (1996) An exact integral equation for solitary waves (with new numerical results for some 'internal' properties). Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 452 (1945). pp. 373-390. ISSN 1364-5021. (The full text of this publication is not available from this repository)

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Abstract

A novel exact within potential flow integral equation for the solitary wave profile, n(s)(X), is presented and numerically solved utilizing a parametric form for the profile and 'tailored quadrature' methods. We believe the profiles and properties of such waves, so obtained, to be the most accurate (to date). From the profiles, certain internal properties of interest, such as the shapes and properties of internal streamlines, internal velocities and pressures, that appear to be hitherto unevaluated in the literature, are here presented. In the outskirts, it is shown that the Stokes form for the exponential decay, n(s)(X) similar to e(-mu x/h), of the surface profile is also valid for all streamlines. The amplitude of this exponential decay is numerically obtained for all solitary wave surface profiles. The analagous decay amplitude of an internal streamline is shown to be related to the surface profile amplitude via a simple quadrature. Like several other properties of solitary waves, it is found that the surface profile outskirts decay amplitude, as well as the pressure on the canal bed directly underneath the crest, are largest for waves of lesser height than the 'maximum' wave.

Item Type: Article
Subjects: Q Science > QC Physics
Divisions: Faculties > Science Technology and Medical Studies > School of Physical Sciences
Depositing User: R.F. Xu
Date Deposited: 09 Jun 2009 14:32
Last Modified: 16 Jun 2014 13:27
Resource URI: http://kar.kent.ac.uk/id/eprint/19166 (The current URI for this page, for reference purposes)
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