Journal of Fluid Mechanics

A new type of three-dimensional deep-water wave of permanent form

Philip G.  Saffman a1 and Henry C.  Yuen a2
a1 Applied Mathematics, California Institute of Technology, Pasadena, California 91125
a2 Fluid Mechanics Department, TRW Defense and Space Systems Group, Redondo Beach, California 90278

Article author query
saffman pg   [Google Scholar] 
yuen hc   [Google Scholar] 


A new class of three-dimensional, deep-water gravity waves of permanent form has been found using an equation valid for weakly nonlinear waves due to Zakharov (1968). These solutions appear as bifurcations from the uniform two-dimensional wave train. The critical wave heights are given as functions of the modulation wave vector. The three-dimensional patterns may be skewed or symmetrical. An example of the skewed wave pattern is given and shown to be stable. The results become exact in the limit of very oblique modulations.

(Published Online April 19 2006)
(Received January 7 1980)
(Revised April 14 1980)