Reynolds number dependence of Lagrangian dispersion in direct numerical simulations of anisotropic magnetohydrodynamic turbulence

Abstract

Large-scale magnetic fields thread through the electrically conducting matter of the interplanetary and interstellar medium, stellar interiors, and other astrophysical plasmas, producing anisotropic flows with regions of high-Reynolds-number turbulence. It is common to encounter turbulent flows structured by a magnetic field with a strength approximately equal to the root-mean-square magnetic fluctuations. In this work, direct numerical simulations of anisotropic magnetohydrodynamic (MHD) turbulence influenced by such a magnetic field are conducted for a series of cases that have identical resolution, and increasing grid sizes up to $2048^3$. The result is a series of closely comparable simulations at Reynolds numbers ranging from 1,400 up to 21,000. We investigate the influence of the Reynolds number from the Lagrangian viewpoint by tracking fluid particles and calculating single-particle and two-particle statistics. The influence of Alfvénic fluctuations and the fundamental anisotropy on the MHD turbulence in these statistics is discussed. Single-particle diffusion curves exhibit mildly superdiffusive behaviors that differ in the direction aligned with the magnetic field and the direction perpendicular to it. Competing alignment processes affect the dispersion of particle pairs, in particular at the beginning of the inertial subrange of time scales. Scalings for relative dispersion, which become clearer in the inertial subrange for larger Reynolds number, can be observed that are steeper than indicated by the Richardson prediction.

arXiv comment23 pages, 11 figures

References in corpus (28)

• Spectrum of magnetohydrodynamic turbulence
• The Anisotropy of MHD Alfvénic Turbulence
• The Universality of Turbulence in Galactic Molecular Clouds
• Simulations of MHD Turbulence in a Strongly Magnetized Medium
• Turbulent molecular clouds
• The Millennium Arecibo 21-cm Absorption Line Survey. IV. Statistics of Magnetic Field, Column Density, and Turbulence
• On the Spectrum of Magnetohydrodynamic Turbulence
• Spectral energy dynamics in magnetohydrodynamic turbulence
• Strong Anisotropic MHD Turbulence with Cross Helicity
• Lagrangian statistics of particle pairs in homogeneous isotropic turbulence
• A statistical model of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence
• On weak and strong magnetohydrodynamic turbulence
• Refined critical balance in strong Alfvenic turbulence
• Anisotropy of third-order structure functions in MHD turbulence
• Turbulent pair dispersion as a ballistic cascade phenomenology
• The inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
• 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
• The Inherently Three-Dimensional Nature of Magnetized Plasma Turbulence
• The Origin of Interstellar Turbulence in M33
• Two-Particle Dispersion in Model Velocity Fields
• Transition from weak to strong cascade in MHD turbulence
• Varying the forcing scale in low Prandtl number dynamos
• Scaling properties of small-scale fluctuations in magnetohydrodynamic turbulence
• Residual energy in magnetohydrodynamic turbulence and in the solar wind
• Comparison of forcing functions in magnetohydrodynamic turbulence
• Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection
• The Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics