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Stability Of Fully Nonlinear Stokes Waves On Deep Water: Part 1. Perturbation Theory, Shahrdad Sajjadi, David L. Ross

Publications

We consider a full set of harmonics for the Stokes wave in deep water in the absence of viscosity, and examine the role that higher harmonics play in modifying the classical Benjamin-Feir instability. Using a representation of the wave coefficients due to Wilton, a perturbation analysis shows that the Stokes wave may become unbounded due to interactions between the N^th harmonic of the primary wave train and a set of harmonics of a disturbance. If the frequency of the n^th harmonic is denoted Ꙍ_n = Ꙍ(1 ± ꭉ) then instability will occur if

√2 k n^{n …}