Random matrix model of Kolmogorov-Zakharov turbulence
arXiv:2401.11545 · doi:10.1103/PhysRevE.109.044201
Abstract
We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite size system with many degrees of freedom. For the case of a direct cascade the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.
11 pages, 9 figures, update with published version
References in corpus (15)
- Anderson Transitions
- Destruction of Anderson localization by a weak nonlinearity
- Fermi, Pasta, Ulam and a mysterious lady
- Delocalization induced by nonlinearity in systems with disorder
- Statistical mechanics of beam self-cleaning in GRIN multimode optical fibers
- Thermalization of orbital angular momentum beams in multimode optical fibers
- Observation of light thermalization to negative temperature Rayleigh-Jeans equilibrium states in multimode optical fibers
- Nonlinear lattice waves in heterogeneous media
- Direct and inverse cascades in turbulent Bose-Einstein condensate
- Interplay of thermalization and strong disorder: Wave turbulence theory, numerical simulations, and experiments in multimode optical fibers
- Nonlinear delocalization on disordered Stark ladder
- Impact of cavity geometry on microlaser dynamics
- Kolmogorov turbulence, Anderson localization and KAM integrability
- Random lasing from Anderson attractors
- Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model