Random matrix model of Kolmogorov-Zakharov turbulence
arxiv(2024)
摘要
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.
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