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Daytona Beach


Physical Sciences

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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 Nth harmonic of the primary wave train and a set of harmonics of a disturbance. If the frequency of the nth harmonic is denoted n = Ꙍ(1 ± ꭉ) then instability will occur if

√2 k nn sn

0 < ꭉ < (n -1) !

subject to the disturbance initially having sufficiently large amplitude. We show that, subject to initial conditions, all lower harmonics will contribute to instability as well, and we identify the frequency of the disturbance corresponding to maximum growth rate.

Publication Title

Advances and Applications in Fluid Mechanics


Pushpa Publishing