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Oblique instability of periodic waves in shallow water

Published online by Cambridge University Press:  12 April 2006

P. J. Bryant
P. J. Bryant
Affiliation:
Mathematics Department, University of Canterbury, Christchurch, New Zealand
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Abstract

Periodic permanent waves in shallow water are stable to periodic disturbances in the same direction, but are unstable to certain oblique periodic disturbances. A computer-assisted stability analysis is made of such waves for oblique disturbances with wavelengths comparable to and long compared with the fundamental wavelength. Regions of instability are calculated, and an explanation is given for the occurrence of instability. It is shown that disturbances in the same direction with a small margin of stability may cause a greater modification to the permanent wave in practice than do oblique unstable disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 4 , 28 June 1978 , pp. 783 - 792
Copyright
© 1978 Cambridge University Press

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References

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