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Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train

Published online by Cambridge University Press:  12 April 2006

Bruce M. Lake ,
Henry C. Yuen ,
Harald Rungaldier  and
Warren E. Ferguson
Bruce M. Lake
Affiliation:
Fluid Mechanics Department, TRW/DSSG, One Space Park, Redondo Beach, California 90278
Henry C. Yuen
Affiliation:
Fluid Mechanics Department, TRW/DSSG, One Space Park, Redondo Beach, California 90278
Harald Rungaldier
Affiliation:
Fluid Mechanics Department, TRW/DSSG, One Space Park, Redondo Beach, California 90278
Warren E. Ferguson
Affiliation:
Fluid Mechanics Department, TRW/DSSG, One Space Park, Redondo Beach, California 90278 Permanent address: Department of Mathematics, University of Arizona, Tucson, Arizona 85712.
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Abstract

Results of an experimental investigation of the evolution of a nonlinear wave train on deep water are reported. The initial stage of evolution is found to be characterized by exponential growth of a modulational instability, as was first discovered by Benjamin ' Feir. At later stages of evolution it is found that the instability does not lead to wave-train disintegration or loss of coherence. Instead, the modulation periodically increases and decreases, and the wave train exhibits the Fermi–Pasta–Ulam recurrence phenomenon. Results of an earlier study of nonlinear wave packets by Yuen ' Lake, in which solutions of the nonlinear Schrödinger equation were shown to provide quantitatively correct descriptions of the properties of nonlinear wave packets, are applied to describe the experimentally observed wave-train phenomena. A comparison between the laboratory data and numerical solutions of the nonlinear Schrödinger equation for the long-time evolution of nonlinear wave trains is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 1 , 1 November 1977 , pp. 49 - 74
Copyright
© 1977 Cambridge University Press

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