Structures and Lagrangian statistics of the Taylor-Green Dynamo

Abstract

The evolution of a Taylor-Green forced magnetohydrodynamic (MHD) system showing dynamo activity is analyzed via direct numerical simulations. The statistical properties of the velocity and magnetic field in Eulerian coordinates and along trajectories of fluid elements (Lagrangian coordinates) are found to change between the kinematic, non-linear and saturated regime. Fluid element (tracer) trajectories change from chaotic quasi-isotropic (kinematic phase) to mean magnetic field aligned (saturated phase). The probability density functions (PDFs) of the magnetic field change from strongly non-Gaussian in the kinematic to quasi-Gaussian PDFs in the saturated regime so that their flatness give a precise handle on the definition of the limiting points of the three regimes. Also the statistics of the fluctuations of the kinetic and magnetic energy along fluid trajectories change. All this goes along with a dramatic increase of the correlation time of velocity and magnetic field fluctuations experienced by tracers significantly exceeding one turbulent large-eddy turn-over time. A remarkable consequence is an intermittent scaling regime of the Lagrangian magnetic field structure functions at unusually long time scales.

References in corpus (21)

• Spectrum of magnetohydrodynamic turbulence
• Fluid Particle Accelerations in Fully Developed Turbulence
• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Small Scale Energy Cascade of the Solar Wind Turbulence
• Magnetic Field Saturation in the Riga Dynamo Experiment
• Acceleration statistics of heavy particles in turbulence
• Multifractal statistics of Lagrangian velocity and acceleration in turbulence
• Shell to shell energy transfer in MHD, Part I: steady state turbulence
• Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation
• Numerical study of dynamo action at low magnetic Prandtl numbers
• Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
• Long time correlations in Lagrangian dynamics: a key to intermittency in turbulence
• Slow dynamics in a turbulent von Kármán swirling flow
• Dynamo regimes and transitions in the VKS experiment
• Dynamo action at low magnetic Prandtl numbers: mean flow vs. fully turbulent motion
• Impact of the floating-point precision and interpolation scheme on the results of DNS of turbulence by pseudo-spectral codes
• Lagrangian Statistics of Navier-Stokes- and MHD-Turbulence
• Transition from large-scale to small-scale dynamo
• Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics
• A Lagrangian model for the evolution of turbulent magnetic and passive scalar fields
• Clustering of passive impurities in MHD turbulence

Cited by in corpus (3)

• Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence
• Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations
• Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection