For orthogonal swell and wind waves we find evidence that there is almost no significant change in the probability of freak waves in the wind sea. We find evidence that a realistic short-crested wind sea can on average experience a small increase in freak wave probability because of a swell provided the swell is not orthogonal to the wind waves. Numerical Monte Carlo simulations of the long-term evolution of a spectrum of short waves in the presence of a monochromatic swell are employed to extract statistical distributions of freak waves among the short waves. 565–583) for the modulation of a short wave riding on a longer wave. The swell-modified equation is solved analytically to yield an extended version of the result of Longuet-Higgins & Stewart ( J. Starting from Zakharov's spectral formulation, we derive a new modified nonlinear Schrödinger equation appropriate for the nonlinear evolution of a narrow-banded spectrum of short waves influenced by a swell. The effect of a swell on the statistical distribution of a directional short-wave field is investigated.
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