Shear Photospheric Forcing and the Origin of Turbulence in Coronal Loops

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 magnetohydrodynamics 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 1D 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-lines footpoints follow but they rather stem from the inherent nonlinear nature of the system.

Coronal heating and nanoflares: current sheet formation and heating

“…(20) our parameter λ = d/L. However, if η 0, then the solution (as also shown by Rappazzo et al (2010)) is Figure 1 shows B y (t) for three values of η and for ideal MHD. Obviously, ifηd is small, then solution (24) agrees with the ideal evolution of (23).…”

“…Recently, using reduced magnetohydrodynamics (MHD), Rappazzo et al (2007Rappazzo et al ( , 2008Rappazzo et al ( , 2010 have investigated the formation and evolution of current sheets and the cascade of energy to small-scales. In their system which is continuously driven at the photospheric boundary, they study the turbulent cascade of energy injected at large photospheric scales down to its dissipation at numerous current layers at the small scale.…”

“…Another difference to Galsgaard & Nordlund (1996b) is that we do not consider multiple random shearing of the uniform field, instead just two shears are preformed in our experiments. These create a single initial current layer, as opposed to the many transient current accumulations seen in Galsgaard & Nordlund (1996b), Rappazzo et al (2010) and Dahlburg et al (2012). By looking closely at the energetics of our single current layer system we investigate whether the dissipation of such a layer provides sufficient energy for either a single nanoflare on its own or many nanoflares when the system is continuously driven.…”

Stochastic Coupling of Solar Photosphere and Corona

“…The energy is initially injected at the largest scale is due to, e.g., photospheric motions. Next, nonlinear effects in the corona transfer this energy to ever smaller scales, similarly to the generation of multiscale eddies in turbulent fluids (Dmitruk & Gomez 1997;Buchlin et al 2003;Nigro et al 2004;Buchlin et al 2003Buchlin et al , 2005Buchlin & Velli 2007;Rappazzo et al 2010). Intermittent turbulence can generate SOC-like probability distributions of dissipative events coexisting with traditional fluid signatures, such as power-law scaling of structure functions (Uritsky et al 2007).…”

Evidence for Nonlinear Development of Magnetohydrodynamic Scale Intermittency in the Inner Heliosphere

“…On the other hand, it would be difficult to imagine that the turbulence and structures seen in the lower corona are Gaussian and incoherent. Instead, lower coronal turbulence appears to be highly intermittent (Dmitruk et al 1998;Rappazzo et al 2010). Therefore, the present suggestion is that the way in which the solar wind is processed through the trans-Alfvénic region acts to destroy coherence, which then is dynamically built up again through nonlinear interactions in the super-Alfvénic wind.…”