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Soliton models of long internal waves

Published online by Cambridge University Press:  20 April 2006

Harvey Segur  and
J. L. Hammack
Harvey Segur
Affiliation:
Aeronautical Research Associates of Princeton, Inc., P.O. Box 2229, Princeton, New Jersey 08540, U.S.A.
J. L. Hammack
Affiliation:
Department of Civil Engineering, University of California, Berkeley, California 94720, U.S.A. Present address: Dept of Engng Sciences, University of Florida, Gainesville, Fla 32611.
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Abstract

The Korteweg-de Vries (KdV) equation and the finite-depth equation of Joseph (1977) and Kubota, Ko & Dobbs (1978) both describe the evolution of long internal waves of small but finite amplitude, propagating in one direction. In this paper, both theories are tested experimentally by comparing measured and theoretical soliton shapes. The KdV equation predicts the shapes of our measured solitons with remarkable accuracy, much better than does the finite-depth equation. When carried to second-order, the finite-depth theory becomes about as accurate as (first-order) KdV theory for our experiments. However, second-order corrections to the finite-depth theory also identify a bound on the range of validity of that entire expansion. This range turns out to be rather small; it includes only about half of the experiments reported by Koop & Butler (1981).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 118 , May 1982 , pp. 285 - 304
Copyright
© 1982 Cambridge University Press

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