The Instability and Breaking of a Deep-Water Wave Train

  • W. K. Melville


We report measurements of the surface displacement and fluid velocity in a nonlinear deep- water wave train as it evolved to breaking. Two distinct regimes are found. For ak 0.29 the evolution is sensibly two-dimensional with the Benjamin-Feir instability leading directly to breaking as found by Longuet-Higgins and Cokelet (1978). The measured frequency of the most unstable sideband agrees very well with the predictions of Longuet-Higgins (1978). The surface displacement spectrum is not restricted to a few discrete frequencies but also involves a growing continuous spectrum. Within the accuracy of the measurements, the onset of breaking corresponds to the onset of the asymmetric development of the sidebands about the fundamental frequency. It is suggested that the asymmetric evolution, which ultimately leads to the shift to lower frequency (Lake et al, 1977), may be related to Longuet-Higgins’s (1978) breaking instabihty. For ak ⩾ 0.31 a full three-dimensional instability dominates the Benjamin-Feir instability and leads rapidly to breaking. Preliminary measurements of this instability agree very well with the results of McLean et al. (1981). Continuous measurements of the velocity field at the fluctuating surface were made with a laser anemometer and show significant differences between the velocity field in unbroken and breaking waves. In the unbroken waves the measured velocity agrees very well with that inferred by the measured surface displacement. In breaking waves the velocity in the spilling region is comparable to the phase speed of the waves while the perturbation to the surface displacement is small. With the exception of the velocity measurements, this work is reported by Melville (1982). The velocity measuring technique and analyzed data will be reported elsewhere (Melville and Rapp, 1985).


Wave Train Surface Displacement Breaking Wave Surface Velocity Field Measured Surface Displacement 
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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • W. K. Melville
    • 1
    • 2
  1. 1.Institute of Geophysics and Planetary PhysicsUniversity of CaliforniaSan DiegoUSA
  2. 2.Department of Civil EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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