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arXiv · 1611.08030

4-wave dynamics in kinetic wave turbulence

Sergio Chibbaro·Giovanni Dematteis·Lamberto Rondoni
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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 $Z$ 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 $Z$. 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 $N$-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency.

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Sergio Chibbaro, Giovanni Dematteis, Lamberto Rondoni. 2016-11-23. 4-wave dynamics in kinetic wave turbulence. https://arxiv.org/abs/1611.08030

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