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The solitary wave in water of variable depth

Published online by Cambridge University Press:  29 March 2006

R. Grimshaw
R. Grimshaw
Affiliation:
University of Melbourne
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Abstract

Equations are derived for two-dimensional long waves of small, but finite, amplitude in water of variable depth, analogous to those derived by Boussinesq for water of constant depth. When the depth is slowly varying compared to the length of the wave, an asymptotic solution of these equations is obtained which describes a slowly varying solitary wave; also differential equations for the slow variations of the parameters describing the solitary wave are derived, and solved in the case when the solitary wave evolves from a region of uniform depth. For small amplitudes it is found that the wave amplitude varies inversely as the depth.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 3 , 9 July 1970 , pp. 639 - 656
Copyright
© 1970 Cambridge University Press

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