Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation
Abstract
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 secondorder phase transition. The results corroborate the experimental observations of Banner, Babanin, and Young [J. Phys. Oceanogr. 30, 3145 (2000)JPYOBT0022367010.1175/15200485(2000)030<3145:BPFDWO>2.0.CO;2].
 Publication:

Physical Review Letters
 Pub Date:
 October 2007
 DOI:
 10.1103/PhysRevLett.99.164501
 arXiv:
 arXiv:0705.2838
 Bibcode:
 2007PhRvL..99p4501Z
 Keywords:

 47.27.ek;
 47.35.Jk;
 Direct numerical simulations;
 Wave breaking;
 Physics  Atmospheric and Oceanic Physics;
 Physics  Computational Physics;
 Physics  Fluid Dynamics
 EPrint:
 5 pages, 5 figures, Submitted in Phys. Rev. Letters