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Water waves in a deep square basin

Published online by Cambridge University Press:  26 April 2006

Peter J. Bryant  and
Michael Stiassnie
Peter J. Bryant
Affiliation:
Department of Mathematics and Statistics, University of Canterbuty, Christchurch, New Zealand
Michael Stiassnie
Affiliation:
Coastal and Marine Engineering Research Institute, Department of Civil Engineering Technion-Israel Institute of Techology, Haifa 32000, Israel
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Abstract

The form and evolution of three-dimensional standing waves in deep water are calculated analytically from Zakharov's equation and computationally from the full nonlinear bounddary value problem. The water is contained in a basin with a square cross-cection, when three-dimensional properties to pairs of sides are the same. It is found that non-periodic standing waves commonly follow forms of cyclic recurrence over times. The two-dimensional Stokes type of periodic standing waves (dominated by the fundamental harmonic) are shown to be unstable to three dimensional disturbances, but over long times the waves return cyclically close to their initial state. In contrast, the three-dimensional Stokes type of periodic standing waves are found to be stabel to small disturbances. New two-dimensional periodic standing waves with amplitude maxima at other than the fundamental harmonic have been investigated recently (Bryant & Stiassnie 1994). The equivalent three-dimensional standing waves are described here. The new two-dimensional periodic standing waves, like the two-dimensional Stokes standing waves, are found to be unstable to three-dimensional disturbances, and to exhibit cyclic recurrence over long times. Only some of the new three-dimensional periodic standing waves are found to be stable to small disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 302 , 10 November 1995 , pp. 65 - 90
Copyright
© 1995 Cambridge University Press

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References

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