Abstract
We have derived an equation governing the evolution of a random field of nonlinear, deep-water, gravity waves by extending the approach used by Zakharov [1] for describing the deterministic system. This equation accounts for both the effects of inhomogeneity and the energy transfer mechanism associated with the homogeneous spectrum. The narrow-band limit of this equation is used to study the stability of a random wavetrain to two-dimensional deterministic perturbations. The effect of randomness is found to reduce the growth rate and the extent of the instability.
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