Shell Models of RMHD Turbulence and the Heating of Solar Coronal Loops

A simplified non-linear numerical model for the development of incompressiblemagnetohydrodynamics (MHD) in the presence of a strong magnetic field B0 andstratification, nicknamed Shell-Atm, is presented. In planes orthogonal to themean field, the non-linear incompressible dynamics is replaced by 2Dshell-models for the complex variables u and b, allowing one to reach largeReynolds numbers while at the same time carrying out sufficiently long timeintegrations to obtain a good statistics at moderate computational cost. Theshell-models of different planes are coupled by Alfven waves propagating alongB0. The model may be applied to open or closed magnetic field configurationswhere the axial field dominates and the plasma pressure is low; here we applyit to the specific case of a magnetic loop of the solar corona heated viaturbulence driven by photospheric motions, and we use statistics for itsanalysis. The Alfven waves interact non-linearly and form turbulent spectra inthe directions perpendicular and, via propagation, also parallel to the meanfield. A heating function is obtained, and is shown to be intermittent; theaverage heating is consistent with values required for sustaining a hot corona,and is proportional to the aspect ratio of the loop to the power -1.5;characteristic properties of heating events are distributed as power-laws.Cross-correlations show a delay of dissipation compared to energy content.Comment: 12 pages, 16 figures, accepted for publication in Ap