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Reflections from solitary waves in channels of decreasing depth

Published online by Cambridge University Press:  20 April 2006

C. J. Knickerbocker  and
Alan C. Newell
C. J. Knickerbocker
Affiliation:
St Lawrence University, Department of Mathematics, Canton, NY 13617
Alan C. Newell
Affiliation:
Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721
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Abstract

We have found that the reflected wave that is created by a right-going solitary wave as it travels in a region of slowly changing depth does not satisfy Green's law. The amplitude of the reflected wave is constant along left-going characteristics rather than proportional to the negative fourth root of depth. This new finding allows us to satisfy the mass-flux conservation laws to leading order and establishes that the perturbed Korteweg–de Vries equation is a consistent approximation for the right-going profile.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 153 , April 1985 , pp. 1 - 16
Copyright
© 1985 Cambridge University Press

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References

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