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Periodic waves in shallow water

Published online by Cambridge University Press:  29 March 2006

P. J. Bryant
P. J. Bryant
Affiliation:
Fluid Mechanics Research Institute, University of Essex, Colchester, Essex
Permanent address: Mathematics Department, University of Canterbury, Christchurch, New Zealand.
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Abstract

An investigation is made into the evolution, from a sinusoidal initial wave train, of long periodic waves of small but finite amplitude propagating in one direction over water in a uniform channel. The spatially periodic surface displacement is expanded in a Fourier series with time-dependent coefficients. Equations for the Fourier coefficients are derived from three sources, namely the Korteweg–de Vries equation, the regularized long-wave equation proposed by Benjamin, Bona & Mahony (1972) and the relevant nonlinear boundary-value problem for Laplace's equation. Solutions are found by analytical and by numerical methods, and the three models of the system are compared. The surface displacement is found to take the form of an almost linear superposition of wave trains of the same wavelength as the initial wave train.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 4 , 7 August 1973 , pp. 625 - 644
Copyright
© 1973 Cambridge University Press

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References

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