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

On the two-dimensional state in driven magnetohydrodynamic turbulence

The dynamics of the two-dimensional (2D) state in driven tridimensional (3D) incompressible magnetohydrodynamic turbulence is investigated through high-resolution direct numerical simulations and in the presence of an external magnetic field at various intensities. For such a flow the 2D state (or slow mode) and the 3D modes correspond respectively to spectral fluctuations in the plan $k_\parallel=0$ and in the area $k_\parallel>0$. It is shown that if initially the 2D state is set to zero it becomes non negligible in few turnover times particularly when the external magnetic field is strong. The maintenance of a large scale driving leads to a break for the energy spectra of 3D modes; when the driving is stopped the previous break is removed and a decay phase emerges with alfv\'enic fluctuations. For a strong external magnetic field the energy at large perpendicular scales lies mainly in the 2D state and in all situations a pinning effect is observed at small scales.Comment: 11 pages, 11 figure

Finite dissipation and intermittency in magnetohydrodynamics

We present an analysis of data stemming from numerical simulations of decaying magnetohydrodynamic (MHD) turbulence up to grid resolution of 1536^3 points and up to Taylor Reynolds number of 1200. The initial conditions are such that the initial velocity and magnetic fields are helical and in equipartition, while their correlation is negligible. Analyzing the data at the peak of dissipation, we show that the dissipation in MHD seems to asymptote to a constant as the Reynolds number increases, thereby strengthening the possibility of fast reconnection events in the solar environment for very large Reynolds numbers. Furthermore, intermittency of MHD flows, as determined by the spectrum of anomalous exponents of structure functions of the velocity and the magnetic field, is stronger than for fluids, confirming earlier results; however, we also find that there is a measurable difference between the exponents of the velocity and those of the magnetic field, as observed recently in the solar wind. Finally, we discuss the spectral scaling laws that arise in this flow.Comment: 4 pages, 4 figure

Phenomenology for the decay of energy-containing eddies in homogeneous MHD turbulence

We evaluate a number of simple, one‐point phenomenological models for the decay of energy‐containing eddies in magnetohydrodynamic(MHD) and hydrodynamicturbulence. The MHDmodels include effects of cross helicity and Alfvénic couplings associated with a constant mean magnetic field, based on physical effects well‐described in the literature. The analytic structure of three separate MHDmodels is discussed. The single hydrodynamic model and several MHDmodels are compared against results from spectral‐method simulations. The hydrodynamic model phenomenology has been previously verified against experiments in wind tunnels, and certain experimentally determined parameters in the model are satisfactorily reproduced by the present simulation. This agreement supports the suitability of our numerical calculations for examining MHDturbulence, where practical difficulties make it more difficult to study physical examples. When the triple‐decorrelation time and effects of spectral anisotropy are properly taken into account, particular MHDmodels give decay rates that remain correct to within a factor of 2 for several energy‐halving times. A simple model of this type is likely to be useful in a number of applications in space physics, astrophysics, and laboratory plasma physics where the approximate effects of turbulence need to be included

Coronal heating in coupled photosphere-chromosphere-coronal systems: turbulence and leakage

Coronal loops act as resonant cavities for low frequency fluctuations that are transmitted from the deeper layers of the solar atmosphere and are amplified in the corona, triggering nonlinear interactions. However trapping is not perfect, some energy leaks down to the chromosphere, thus limiting the turbulence development and the associated heating. We consider the combined effects of turbulence and leakage in determining the energy level and associated heating rate in models of coronal loops which include the chromosphere and transition region. We use a piece-wise constant model for the Alfven speed and a Reduced MHD - Shell model to describe the interplay between turbulent dynamics in the direction perpendicular to the mean field and propagation along the field. Turbulence is sustained by incoming fluctuations which are equivalent, in the line-tied case, to forcing by the photospheric shear flows. While varying the turbulence strength, we compare systematically the average coronal energy level (E) and dissipation rate (D) in three models with increasing complexity: the classical closed model, the semi-open corona model, and the corona-chromosphere (or 3-layer) model, the latter two models allowing energy leakage. We find that: (i) Leakage always plays a role (even for strong turbulence), E and D are systematically lower than in the line-tied model. (ii) E is close to the resonant prediction, i.e., assuming effective turbulent correlation time longer than the Alfven coronal crossing time (Ta). (iii) D is close to the value given by the ratio of photospheric energy divided by Ta (iv) The coronal spectra exibits an inertial range with 5/3 spectral slope, and a large scale peak of trapped resonant modes that inhibit nonlinear couplings. (v) In the realistic 3-layer model, the two-component spectrum leads to a damping time equal to the Kolmogorov time reduced by a factor u_rms/Va_coronaComment: 15 pages, 15 figures, Accepted for publication in A&

Spectral energy dynamics in magnetohydrodynamic turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to $1024^3$ collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, $E_k^\mathrm{R}=|E_k^\mathrm{M}-E_k^\mathrm{K}|$, and total energy, $E_k=E^\mathrm{K}_k+E^\mathrm{M}_k$, are observed to scale self-similarly in the inertial range as $E_k^\mathrm{R}\sim k^{-7/3}$, $E_k\sim k^{-5/3}$ (isotropic case) and $E^\mathrm{R}_{k_\perp}\sim k_\perp^{-2}$, $E_{k_\perp}\sim k_\perp^{-3/2}$ (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasi-normal Markovian (EDQNM) closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfv\'en effect yields $E_k^\mathrm{R}\sim k E^2_k$ which is confirmed by the simulations.Comment: accepted for publication by PR

Strong Imbalanced Turbulence

We consider stationary, forced, imbalanced, or cross-helical MHD Alfvenic turbulence where the waves traveling in one direction have higher amplitudes than the opposite waves. This paper is dedicated to so-called strong turbulence, which cannot be treated perturbatively. Our main result is that the anisotropy of the weak waves is stronger than the anisotropy of a strong waves. We propose that critical balance, which was originally conceived as a causality argument, has to be amended by what we call a propagation argument. This revised formulation of critical balance is able to handle the imbalanced case and reduces to old formulation in the balanced case. We also provide phenomenological model of energy cascading and discuss possibility of self-similar solutions in a realistic setup of driven turbulence.Comment: this is shorter, 5 page version of what is to appear in ApJ 682, Aug. 1, 200