Chaotic behavior of Eulerian MHD turbulence
arXiv:1808.03632 · doi:10.1063/1.5092367
Abstract
We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We extend the Ruelle theory of hydrodynamic turbulence to magnetohydrodynamic turbulence as a working hypothesis and find broad agreement with results. In other simulations we introduce magnetic helicity and these simulations show a diminution of chaos, which is expected to be eliminated at maximum helicity. We also find that the difference between two initially close fields grows linearly at late times, which was also recently found in hydrodynamics. This linear growth rate is found to be dependent on the dissipation rate of the relevant field. We discuss the important consequences this linear growth has on predictability. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas.
arXiv comment11 pages, 7 figures. In Press Physics of Plasmas, 2019
References in corpus (24)
- Control of star formation by supersonic turbulence
- Astrophysical magnetic fields and nonlinear dynamo theory
- The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
- The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds
- Cascades and transitions in turbulent flows
- Predictability in the large: an extension of the concept of Lyapunov exponent
- Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas
- Lagrangian statistics of particle pairs in homogeneous isotropic turbulence
- Thermodynamic ground states of platinum metal nitrides
- On the Magnetic Prandtl Number Behavior of Accretion Disks
- On the inverse cascade of magnetic helicity
- Turbulent Pumping of Magnetic Flux Reduces Solar Cycle Memory and thus Impacts Predictability of the Sun's Activity
- Magnetic Prandtl number dependence of kinetic to magnetic dissipation ratio
- Chaos and predictability of homogeneous-isotropic turbulence
- Chaotic properties of a turbulent isotropic fluid
- Scaling of Lyapunov Exponents in Homogeneous Isotropic Turbulence
- Slow and fast dynamics in coupled systems: A time series analysis view
- Predictability of the energy cascade in 2D turbulence
- Sudden relaminarisation and lifetimes in forced isotropic turbulence
- Magnetic helicity and the evolution of decaying magnetohydrodynamic turbulence
- Self-organisation and non-linear dynamics in driven magnetohydrodynamic turbulent flows
- Comparison of forcing functions in magnetohydrodynamic turbulence
- Visco-resistive MHD study of internal kink(m=1) modes
- Fully resolved array of simulations investigating the influence of the magnetic Prandtl number on magnetohydrodynamic turbulence
Cited by in corpus (5)
- Chaos and information in two dimensional turbulence
- Fluctuations of Lyapunov Exponents in homogeneous and isotropic turbulence
- Information production in homogeneous isotropic turbulence
- Uncertainty Growth in Stably Stratified Turbulence
- Critical transition to a non-chaotic regime in isotropic turbulence