Abstract
Hall effects on local structures in homogeneous, isotropic, and incompressible magnetohydrodynamic turbulence are studied numerically. The transition of vortices from sheet-like to tubular structures induced by the Hall term is found, while the kinetic energy spectrum does not distinguish the two types of structures. It is shown by the use of the sharp low-pass filter that the transition occurs not only in the scales smaller than the ion skin depth but also in a larger scale. The transition is related with the forward energy transfer in the spectral space. Analyses by the use of the sharp low-pass filter show that the nonlinear energy transfer associated with the Hall term is dominated by the forward transfer and relatively local in the wave number space. A projection of the simulation data to a Smagorinsky-type sub-grid-scale model shows that the high wave number component of the Hall term may possibly be replaced by the model effectively.
Highlights
Turbulence is one of the most important keywords in many categories of natural sciences and engineering such as astrophysics, fluid mechanics, and nuclear fusion.Homogeneous magnetohydrodynamic (MHD) turbulence provides a basic framework to study non-linearity, intermittency, and the statistical nature of turbulence
One of the simplest approaches to improve the accuracy of the model is introducing the Hall term to the MHD equations
We focus on the Hall effects on local structures in freely decaying, homogeneous, isotropic, and incompressible Hall MHD turbulence
Summary
Turbulence is one of the most important keywords in many categories of natural sciences and engineering such as astrophysics, fluid mechanics, and nuclear fusion. Matthaeus et al. have reported regarding the alignment of velocity and magnetic field in (single-fluid) MHD turbulence. Reduction of nonlinearity has been studied by the authors from the points of view of the energy transfer functions In spite of these works, elementary structures and their impact on the statistical nature of Hall MHD turbulence are not clarified yet. The symbols ijk ; H ; Re ; Reg denote the Levi-Civita symbol, the Hall parameter (the ion skin depth normalized by the system size), the Reynolds number, and the Lundquist number, respectively These equations are already normalized by some reference quantities. See our previous work for the kinetic and magnetic energy decay Another measure of the development of turbulence is the energy spectra normalized by the Kolmogorov length scale. III, it turns out that a larger qualitative change is observed more in local structures of the velocity field (or the vorticity field, equivalently)
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