Abstract
We present a series of numerical simulations aimed at understanding the nature and origin of turbulence in coronal loops in the framework of the Parker model for coronal heating. A coronal loop is studied via reduced magnetohydrodynamic (MHD) simulations in Cartesian geometry. A uniform and strong magnetic field threads the volume between the two photospheric planes, where a velocity field in the form of a one-dimensional shear flow pattern is present. Initially, the magnetic field that develops in the coronal loop is a simple map of the photospheric velocity field. This initial configuration is unstable to a multiple tearing instability that develops islands with X and O points in the plane orthogonal to the axial field. Once the nonlinear stage sets in the system evolution is characterized by a regime of MHD turbulence dominated by magnetic energy. A well-developed power law in energy spectra is observed and the magnetic field never returns to the simple initial state mapping the photospheric flow. The formation of X and O points in the planes orthogonal to the axial field allows the continued and repeated formation and dissipation of small-scale current sheets where the plasma is heated. We conclude that the observed turbulent dynamics are not induced by the complexity of the pattern that the magnetic field-line footpoints follow but they rather stem from the inherent nonlinear nature of the system.
Highlights
We present a series of numerical simulations aimed at understanding the nature and origin of turbulence in coronal loops in the framework of the Parker model for coronal heating
In recent papers (Rappazzo et al 2007, 2008) we have described reduced magnetohydrodynamics (RMHD) simulations of the Parker problem (Parker 1972, 1988, 1994) for coronal loops in Cartesian geometry
We have shown that the system develops small scales, organized in current sheets elongated in the direction of the DC magnetic field, through an MHD turbulent cascade, and that a well defined power law spectrum is developed for total energy
Summary
In recent papers (Rappazzo et al 2007, 2008) we have described reduced magnetohydrodynamics (RMHD) simulations of the Parker problem (Parker 1972, 1988, 1994) for coronal loops in Cartesian geometry. An analytical model of a forced system very similar to the simulation presented here was proposed by Heyvaerts & Priest (1992), and recently extended to the anisotropic turbulence regime by Bigot et al (2008) They started with same MHD system threaded by a strong axial magnetic field in cartesian geometry and apply at the top and bottom boundaries two 1D velocity fields of opposite direction and assumed that the sheared structure that develops in the corona dissipates via an effective “turbulent resistivity” provided by a cascade, so that a dissipative equilibrium is set up in which shearing is balanced by slippage provided by the turbulence.
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