Journal of Fluid Mechanics

Long wavelength bifurcation of gravity waves on deep water

P. G.  Saffman a1
a1 Applied Mathematics, California Institute of Technology, Pasadena, California 91125

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Conditions are found for the appearance of non-uniform progressive waves of permanent form from a long-wave modulation of a finite-amplitude Stokes wave on deep water. The waveheight at which the modulated waves can occur is a very slowly decreasing function of the modulation wavelength for values up to 150 times the original wavelength. Some qualitative remarks are made about the problem of determining the stability of the new waves.

(Published Online April 19 2006)
(Received December 12 1979)
(Revised April 24 1980)