Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

By performing two parallel numerical experiments—solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation—we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modeling the strongly nonlinear process of white capping. Fitting the two experiments, we determined the dissipation function due to wave breaking and found that it depends very sharply on the parameter of nonlinearity (the surface steepness). The onset of white capping can be compared to a second-order phase transition. The results corroborate the experimental observations of Banner, Babanin, and Young [ J. Phys. Oceanogr. 30 3145 (2000)].