Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

V. E. Zakharov, A. O. Korotkevich, A. Pushkarev, D. Resio
2007 Physical Review Letters  
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 modelling the strongly nonlinear
more » ... ocess 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. This result corroborates with experimental observations by Banner, Babanin, Young.
doi:10.1103/physrevlett.99.164501 pmid:17995256 fatcat:k7dlhojhljfk3pg7om55b4hshy