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The evolution of resonant water-wave oscillations

Published online by Cambridge University Press:  21 April 2006

Edward A. Cox  and
Michael P. Mortell
Edward A. Cox
Affiliation:
Department of Mathematical Physics, University College Dublin, Ireland
Michael P. Mortell
Affiliation:
Registrar's Office, University College Cork, Ireland
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Abstract

This paper is concerned with the evolution of small-amplitude, long-wavelength, resonantly forced oscillations of a liquid in a tank of finite length. It is shown that the surface motion is governed by a forced Korteweg—de Vries equation. Numerical integration indicates that the motion does not evolve to a periodic steady state unless there is dissipation in the system. When there is no dissipation there are cycles of growth and decay reminiscent of Fermi–Pasta–Ulam recurrence. The experiments of Chester & Bones (1968) show that for certain frequencies more than one periodic solution is possible. We illustrate the evolution of two such solutions for the fundamental resonance frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 99 - 116
Copyright
© 1986 Cambridge University Press

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