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Modulation by swell of waves and wave groups on the ocean

Published online by Cambridge University Press:  20 April 2006

P. J. Bryant
P. J. Bryant
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego Permanent address: Mathematics Department, University of Canterbury, Christchurch, New Zealand.
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Abstract

Two of the simpler nonlinear wave systems on water of uniform depth are permanent waves and wave groups of permanent envelope. The interaction of each of these wave systems with swell of much smaller amplitude and greater wavelength, propagating in the same direction, is investigated analytically and numerically. A linear-stability analysis of the modulation of these systems by swell shows that they are unstable over short times. Calculations of their evolution over longer times confirms that the initial exponential growth of the modulations is not sustained, and that cyclic recurrence of the modulations occurs in some cases. The modulation of a wave train by swell is found to concentrate the energy of the wave train into single waves in turn, a process which may cause irreversible nonlinear changes such as wave breaking. In contrast, the only observable effect in the modulation of a wave group by swell is a small slow oscillation of the envelope of the group as it propagates. The conclusion is that wave trains on the ocean, generated for example by a wind system of long fetch and duration, disintegrate under the modulation of swell. Wave groups, however, either wind-generated or resulting from the breakdown of wave trains, propagate almost unchanged by the presence of swell.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 443 - 466
Copyright
© 1972 Cambridge University Press

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