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Modulational development of nonlinear gravity-wave groups

Published online by Cambridge University Press:  20 April 2006

T. K. Chereskin  and
E. Mollo-Christensen
T. K. Chereskin
Affiliation:
Massachusetts Institute of Technology, Department of Meteorology and Physical Oceanography, Cambridge, Massachusetts 02139 Present address: College of Oceanography, Oregon State University, Corvallis, Oregon 97331.
E. Mollo-Christensen
Affiliation:
Massachusetts Institute of Technology, Department of Meteorology and Physical Oceanography, Cambridge, Massachusetts 02139 Present address: NASA, Goddard Space Flight Center, Greenbelt, Maryland 20771.
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Abstract

We present observations of the development of nonlinear surface gravity-wave groups. We calculate the amplitude and phase modulations using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schrödinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation and to test the inviscid predictions for the asymptotic behaviour of groups versus long-time observations. Although dissipation rules out recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behaviour.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 151 , February 1985 , pp. 337 - 365
Copyright
© 1985 Cambridge University Press

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