4-wave dynamics in kinetic wave turbulence
Abstract
A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function is obtained within an "interaction representation" and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for . A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the -mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency.
Cite
@article{arxiv.1611.08030,
title = {4-wave dynamics in kinetic wave turbulence},
author = {Sergio Chibbaro and Giovanni Dematteis and Lamberto Rondoni},
journal= {arXiv preprint arXiv:1611.08030},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1201.4067 by other authors