Distributed chaos in the Hamiltonian dynamical systems and isotropic homogeneous turbulence

TL;DR

This paper explores how distributed chaos in Hamiltonian dynamical systems can resemble turbulence, with numerical simulations showing spectral transitions linked to system smoothness and analytical properties.

Contribution

It demonstrates the connection between distributed chaos in Hamiltonian systems and isotropic turbulence, highlighting the impact of smoothness on spectral behavior and providing analytical insights.

Findings

Distributed chaos in Hamiltonian systems mimics turbulence spectra.

Decrease in smoothness leads to power-law spectra instead of stretched exponentials.

Numerical simulations confirm the spectral transition related to system properties.

Abstract

It is shown that the distributed chaos in the simple Hamiltonian (conservative) dynamical systems, such as the Nose-Hoover oscillator and double oscillator, can mimic the distributed chaos in the isotropic homogeneous turbulence. Direct numerical simulations with the classic Toda lattice and with the nonlinear Schr\"{o}dinger equation (soliton turbulence) under random initial conditions have been also discussed in this context. These properties of the distributed chaos have been related to analytical properties of the Hamiltonian systems. Decrease of the smoothness results in the power-law spectra instead of the stretched exponential ones characteristic to the distributed chaos, both for the dynamical systems and for turbulence.