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A class of elliptical free-surface flows

Published online by Cambridge University Press:  20 April 2006

A. L. New
A. L. New
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, England Present address: Institute of Oceanographic Sciences, Crossway, Taunton, Somerset TA1 2DW.
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Abstract

Exact solutions of the equations of motion for an inviscid fluid are rare. Using the formalism of John (1953), this paper presents a class of exact zero-gravity flows in which the free surface assumes the form of an ellipse having arbitrary but time-constant aspect ratio. The dynamically important region beneath the overturning crest of a breaking gravity wave is examined and the profile is found to be remarkably well approximated by a √3 aspect-ratio ellipse. The range of examples presented includes high-resolution computations in both deep and shallow water, and also the plunger-generated laboratory waves of Miller (1976).

The ellipse solution is shown to model qualitatively certain essential features of the numerical waves. A recent self-similar solution due to Longuet-Higgins (1981, 1982), in which the free surface is a parametric cubic curve, is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 219 - 239
Copyright
© 1983 Cambridge University Press

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