Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

TL;DR

This study compares numerical solutions of Hamiltonian equations and the Hasselmann kinetic equation to evaluate weak turbulence theory's applicability to swell evolution, revealing the importance of nonlinear dissipation effects like white-capping.

Contribution

The paper demonstrates the coexistence of weak and strong turbulence in swell propagation and introduces an empirical dissipation term to match theoretical and numerical results.

Findings

Qualitative agreement between Hamiltonian and kinetic equation results

Dissipation due to white-capping sharply depends on surface steepness

White-capping onset resembles a second-order phase transition

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 modelling 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. This result corroborates with experimental observations by Banner, Babanin, Young.