Abstract
The evolution of a Taylor–Green forced magnetohydrodynamic system showing dynamo activity is analyzed via direct numerical simulations. The statistical properties of the velocity and magnetic fields in Eulerian and Lagrangian coordinates are found to change between the kinematic, nonlinear 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 kinetic and magnetic fluctuations along fluid trajectories changes. All this goes along with a dramatic increase of the correlation time of the velocity and magnetic fields 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.
Highlights
The magnetic field of stars and telluric planets is explained by the dynamo instability, produced by a turbulent conducting fluid where the induction due to the motion takes over the magnetic diffusion
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
Lagrangian statistics has been used in MHD simulations [30, 31] to compare the anomalous exponents of the structure function to their hydrodynamic counterparts and to understand the relation between Eulerian and Lagrangian statistics
Summary
We perform direct numerical simulations of turbulent MHD flows with large-scale forcing in a periodic box. In order to quantify this anisotropy we compute the root mean square (rms) values of the perpendicular (xy-plane) and parallel (z) components of the velocity fields and define the global isotropy coefficient ρiuso as ur⊥ms = [ u2x + u2y /2 ]1/2 , urms = u2z 1/2 , ρiuso = urms/ur⊥ms, ρiBso = Brms/B⊥rms. With these definitions the average rms velocity is urms = [(2 (ur⊥ms)2 + (urms)2)/3]1/2. A detailed list of the physical parameters for the different runs is presented in table 2
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