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Cylindrical solitary waves

Published online by Cambridge University Press:  21 April 2006

P. D. Weidman  and
R. Zakhem
P. D. Weidman
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
R. Zakhem
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
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Abstract

Experiments on the radial propagation of axisymmetric free-surface solitary waves are reported and compared with theoretical and numerical solutions of the cylinderical Korteweg–de Vries (CKdV) equation. A new experimental technique to obtain a continuous amplitude signature on photographic paper is reported. These measurements show that an isolated disturbance evolves into a slowly varying solitary wave with amplitude decaying as $r^{-\frac{2}{3}}$, where r is the radius measured from the centre of the disturbance. A numerical study of the CKdV equation is made to interpret the transient development of these waves into the nonlinear asymptotic regime. It is further pointed out that the CKdV equation also describes weakly nonlinear axisymmetric internal waves, and a comparison of theory for this case with internal-wave trajectory measurements reported by Maxworthy (1980) exhibit good agreement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 191 , June 1988 , pp. 557 - 573
Copyright
© 1988 Cambridge University Press

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