Three Dimensional Stability and Bifurcation of Steady Water Waves

Abstract

The stability of finite amplitude two-dimensional waves of permanent form on deep water to arbitrary three-dimensional disturbances is considered. The possibility of instability is related to the existence of resonances between linear waves. The regions of instability are calculated. It is shown that spontaneous three-dimensional waves of permanent form can arise, from bifurcation of two-dimensional waves at wave heights and wave lengths for which stationary disturbances exist, and their properties are determined.

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