Nonlinear energy transfer to short gravity waves in the presence of long waves

Existing theories for calculating the energy transfer rates to gravity waves due to resonant nonlinear interactions among wave components whose lengths are long in comparison to wave elevations have been verified experimentally and are well accepted. There is uncertainty, however, about prediction of energy transfer rates within a set of waves having short to moderate lengths when these are present simultaneously with a long wave whose amplitude is not small in comparison to the short wavelengths. Here we implement both a direct numerical method that avoids small-amplitude approximations and a spectral method which includes perturbations of high order. These are applied to an interacting set of short- to intermediate-length waves with and without the presence of a large long wave. The same cases are also studied experimentally. Experimentally and numerical results are in reasonable agreement with the finding that the long wave does influence the energy transfer rates. The physical reason for this is identified and the implications for computations of energy transfer to short waves in a wave spectrum are discussed.