Journal of Fluid Mechanics

Wave modulation and breakdown

W. K.  Melville a1
a1 R. M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139 and Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093

Article author query
melville wk   [Google Scholar] 


Time series of amplitude, frequency, wavenumber and phase speed are measured in an unstable deep-water wavetrain using a Hilbert-transform technique. The modulation variables evolve from sinusoidal perturbations that are well described as slowly varying Stokes waves, through increasingly asymmetric modulations that finally result in very rapid jumps or ‘phase reversals’. These anomalies appear to correspond to the ‘crest pairing’ described by Ramamonjiarisoa & Mollo-Christensen (1979). The measurements offer a novel local description of the instability of deep-water waves which contrasts markedly with the description afforded by conventional Fourier decomposition. The measurements display very large local modulations in the phase speed, modulations that may not be anticipated from measurements of the phase speeds of individual Fourier components travelling (to leading order) at the linear phase speed (Lake & Yuen 1978).

(Published Online April 20 2006)
(Received October 6 1981)
(Revised September 7 1982)