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The initial-value problem for long waves of finite amplitude

Published online by Cambridge University Press:  28 March 2006

Robert R. Long
Robert R. Long
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland
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Abstract

Derived herein is a set of partial differential equations governing the propagation of an arbitrary, long-wave disturbance of small, but finite amplitude. The equations reduce to that of Boussinesq (1872) when the assumption is made that the disturbance is propagating in one direction only. The equations are hyperbolic with characteristic curves of constant slope. The initial-value problem can be solved very readily by numerical integration along characteristics. A few examples are included.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 1 , September 1964 , pp. 161 - 170
Copyright
© 1964 Cambridge University Press

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