Shell-models of RMHD turbulence and the heating of solar coronal loops

A simplified non-linear numerical model for the development of incompressible magnetohydrodynamics (MHD) in the presence of a strong magnetic field B0 and stratification, nicknamed Shell-Atm, is presented. In planes orthogonal to the mean field, the non-linear incompressible dynamics is replaced by 2D shell-models for the complex variables u and b, allowing one to reach large Reynolds numbers while at the same time carrying out sufficiently long time integrations to obtain a good statistics at moderate computational cost. The shell-models of different planes are coupled by Alfven waves propagating along B0. The model may be applied to open or closed magnetic field configurations where the axial field dominates and the plasma pressure is low; here we apply it to the specific case of a magnetic loop of the solar corona heated via turbulence driven by photospheric motions, and we use statistics for its analysis. The Alfven waves interact non-linearly and form turbulent spectra in the directions perpendicular and, via propagation, also parallel to the mean field. A heating function is obtained, and is shown to be intermittent; the average 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

Propagation and dissipation of Alfvén waves in stellar atmospheres permeated by isothermal winds

We investigate the nonlinear evolution of Alfvén waves in a radially stratified isothermal atmosphere with wind, from the atmospheric base out to the Alfvénic point. Nonlinear interactions, triggered by wave reflection due to the atmospheric gradients, are assumed to occur mainly in directions perpendicular to the mean radial magnetic field. The nonlinear coupling between waves propagating in opposite directions is modeled by a phenomenological term, containing an integral turbulent length scale, which acts as a dissipative coefficient for waves of a given frequency. Although the wind acceleration profile is not determined self-consistently one may estimate the dissipation rate inside the layer and follow the evolution of an initial frequency spectrum. Reflection of low frequency waves drives dissipation across the whole spectrum, and steeper gradients, i.e. lower coronal temperatures, enhance the dissipation rate. Moreover, when reasonable wave amplitudes are considered, waves of all frequencies damp at the same rate and the spectrum is not modified substantially during propagation. Therefore the sub-Alfvénic coronal layer acts differently when waves interact nonlinearly, no longer behaving as a frequency dependent filter once reflection-generated nonlinear interactions are included, at least within the classes of models discussed here

Non linear evolution of Alfvén wave in the solar atmosphere

We investigate the non-linear evolution of Alfvén waves in the solar atmosphere and wind, from the photosphere out to the Earth’s orbit. Photosphere and chromosphere are modeled as isothermal layers in static equilibrium, connecting across the transition region with a corona and wind. Nonlinear coupling between waves propagating in opposite directions is modeled by a phenomenological term containing an integral turbulent length scale. Spectrum modifications remain similar to what is found in a linear analysis and some characteristic features - i.e. oscillations at higher frequencies- persist despite nonlinear interactions

Heating of coronal loops: weak MHD turbulence and scaling laws

To understand the nonlinear dynamics of the Parker scenario for coronal heating, long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out. A loop is modeled as a box extended along the direction of the strong magnetic field $B_0$ in which the system is embedded. At the top and bottom plates, which represent the photosphere, velocity fields mimicking photospheric motions are imposed. We show that the nonlinear dynamics is described by different regimes of MHD anisotropic turbulence, with spectra characterized by intertial range power laws whose indexes range from Kolmogorov-like values ($\sim 5/3$) up to $\sim 3$. We briefly describe the bearing for coronal heating rates.Comment: 8 pages, 4 figure

Turbulence, Energy Transfers and Reconnection in Compressible Coronal Heating Field-line Tangling Models

MHD turbulence has long been proposed as a mechanism for the heating of coronal loops in the framework of the Parker scenario for coronal heating. So far most of the studies have focused on its dynamical properties without considering its thermodynamical and radiative features, because of the very demanding computational requirements. In this paper we extend this previous research to the compressible regime, including an energy equation, by using HYPERION, a new parallelized, viscoresistive, three-dimensional compressible MHD code. HYPERION employs a Fourier collocation -- finite difference spatial discretization, and uses a third-order Runge-Kutta temporal discretization. We show that the implementation of a thermal conduction parallel to the DC magnetic field induces a radiative emission concentrated at the boundaries, with properties similar to the chromosphere--transition region--corona system.Comment: 4 pages, 4 figures, Solar Wind 12 proceedings (in press

Coupling the solar surface and the corona: coronal rotation, Alfv\'en wave-driven polar plumes

The dynamical response of the solar corona to surface and sub-surface perturbations depends on the chromospheric stratification, and specifically on how efficiently these layers reflect or transmit incoming Alfv\'en waves. While it would be desirable to include the chromospheric layers in the numerical simulations used to study such phenomena, that is most often not feasible. We defined and tested a simple approximation allowing the study of coronal phenomena while taking into account a parametrised chromospheric reflectivity. We addressed the problems of the transmission of the surface rotation to the corona and that of the generation of polar plumes by Alfv\'en waves (Pinto et al., 2010, 2011). We found that a high (yet partial) effective chromospheric reflectivity is required to properly describe the angular momentum balance in the corona and the way the surface differential rotation is transmitted upwards. Alfv\'en wave-driven polar plumes maintain their properties for a wide range of values for the reflectivity, but they become bursty (and eventually disrupt) when the limit of total reflection is attained.Comment: Solar Wind 13: Proceedings of the Thirteenth International Solar Wind Conferenc

Magnetohydrodynamic Turbulent Cascade of Coronal Loop Magnetic Fields

The Parker model for coronal heating is investigated through a high resolution simulation. An inertial range is resolved where fluctuating magnetic energy E_M (k_perp) \propto k_\perp^{-2.7} exceeds kinetic energy E_K (k_\perp) \propto k_\perp^{-0.6}. Increments scale as \delta b_\ell \simeq \ell^{-0.85} and \delta u_\ell \simeq \ell^{+0.2} with velocity increasing at small scales, indicating that magnetic reconnection plays a prime role in this turbulent system. We show that spectral energy transport is akin to standard magnetohydrodynamic (MHD) turbulence even for a system of reconnecting current sheets sustained by the boundary. In this new MHD turbulent cascade, kinetic energy flows are negligible while cross-field flows are enhanced, and through a series of "reflections" between the two fields, cascade more than half of the total spectral energy flow.Comment: 5 pages, 5 figures, to appear in Physical Review E - Rapid. Com