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

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&

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

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

Impact of observational uncertainties on universal scaling of MHD turbulence

Scaling exponents are the central quantitative prediction of theories of turbulence and in-situ satellite observations of the high Reynolds number solar wind flow have provided an extensive testbed of these. We propose a general, instrument independent method to estimate the uncertainty of velocity field fluctuations. We obtain the systematic shift that this uncertainty introduces into the observed spectral exponent. This shift is essential for the correct interpretation of observed scaling exponents. It is sufficient to explain the contradiction between spectral features of the Elsasser fields observed in the solar wind with both theoretical models and numerical simulations of Magnetohydrodynamic turbulence

Nonlinear cascades in two-dimensional turbulent magnetoconvection

The dynamics of spectral transport in two-dimensional turbulent convection of electrically conducting fluids is studied by means of direct numerical simulations (DNS) in the frame of the magnetohydrodynamic (MHD) Boussinesq approximation. The system performs quasi-oscillations between two different regimes of small-scale turbulence: one dominated by nonlinear MHD interactions, the other governed by buoyancy forces. The self-excited change of turbulent states is reported here for the first time. The process is controlled by the ideal invariant cross-helicity, $H^\mathrm{C}=\int_S \mathrm{d}S \mathbf{v}\cdot\mathbf{b}$. The observations are explained by the interplay of convective driving with the nonlinear spectral transfer of total MHD energy and cross-helicity.Comment: 4 pages, 4 figures, accepted for publication in PR

The interplay between helicity and rotation in turbulence: implications for scaling laws and small-scale dynamics

Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of helicity conservation (correlation between velocity and its curl, measuring departures from mirror symmetry) remains unclear since it does not alter the energy spectrum. However, with solid body rotation, significant differences emerge between helical and non-helical flows. We first outline several results, like the energy and helicity spectral distribution and the breaking of strict universality for the individual spectra. Using massive numerical simulations, we then show that small-scale structures and their intermittency properties differ according to whether helicity is present or not, in particular with respect to the emergence of Beltrami-core vortices (BCV) that are laminar helical vertical updrafts. These results point to the discovery of a small parameter besides the Rossby number; this could relate the problem of rotating helical turbulence to that of critical phenomena, through renormalization group and weak turbulence theory. This parameter can be associated with the adimensionalized ratio of the energy to helicity flux to small scales, the three-dimensional energy cascade being weak and self-similar

Numerical solutions of the three-dimensional magnetohydrodynamic alpha-model

We present direct numerical simulations and alpha-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD alpha-model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the alpha-model correctly reproduce the growth rate of magnetic energy during the kinematic regime, but it also captures the nonlinear saturation level and the late generation of a large scale magnetic field by the helical turbulence.Comment: 12 pages, 19 figure

Coherence and Intermittency of Electron Density in Small-Scale Interstellar Turbulence

Spatial intermittency in decaying kinetic Alfven wave turbulence is investigated to determine if it produces non Gaussian density fluctuations in the interstellar medium. Non Gaussian density fluctuations have been inferred from pulsar scintillation scaling. Kinetic Alfven wave turbulence characterizes density evolution in magnetic turbulence at scales near the ion gyroradius. It is shown that intense localized current filaments in the tail of an initial Gaussian probability distribution function possess a sheared magnetic field that strongly refracts the random kinetic Alfven waves responsible for turbulent decorrelation. The refraction localizes turbulence to the filament periphery, hence it avoids mixing by the turbulence. As the turbulence decays these long-lived filaments create a non Gaussian tail. A condition related to the shear of the filament field determines which fluctuations become coherent and which decay as random fluctuations. The refraction also creates coherent structures in electron density. These structures are not localized. Their spatial envelope maps into a probability distribution that decays as density to the power -3. The spatial envelope of density yields a Levy distribution in the density gradient.Comment: 31 pages, 3 figures. Replacement contains short additions to Secs. 6 and