The two-dimensional magnetohydrodynamic Kelvin-Helmholtz instability: compressibility and large-scale coalescence effects

The Kelvin-Helmholtz (KH) instability occurring in a single shear flow configuration that is embedded in a uniform flow-aligned magnetic field, is revisited by means of high resolution two-dimensional (2D) magnetohydrodynamic (MHD) simulations. First, the calculations extend previous studies of magnetized shear flows to a higher compressibility regime. The nonlinear evolution of an isolated KH billow emerging from the fastest growing linear mode for a convective sonic Mach number $M_{cs}=0.7$ layer is in many respects similar to its less compressible counterpart (Mach $M_{cs}=0.5$). In particular, the disruptive regime where locally amplified, initially weak magnetic fields, control the nonlinear saturation process is found for Alfv\'en Mach numbers 4\simlt M_A \simlt 30. The most notable difference between $M_{cs}=0.7$ versus $M_{cs}=0.5$ layers is that higher density contrasts and fast magnetosonic shocklet structures are observed. Second, the use of adaptive mesh refinement allows to parametrically explore much larger computational domains, including up to 22 wavelengths of the linearly dominant mode. A strong process of large-scale coalescence is found, whatever the magnetic field regime. It proceeds through continuous pairing/merging events between adjacent vortices up to the point where the final large-scale vortical structure reaches the domain dimensions. This pairing/merging process is attributed to the growth of subharmonic modes and is mainly controlled by relative phase differences between them. These grid-adaptive simulations demonstrate that even in very weak magnetic field regimes ($M_A \simeq 30$), the large-scale KH coalescence process can trigger tearing-type reconnection events previously identified in cospatial current-vortex sheets.Comment: Published in Physics of Plasmas, figures absent due to file sizes, full version at http://www.phys.uu.nl/~toth/ (follow Publications

A Nanoflare Distribution Generated by Repeated Relaxations Triggered by Kink Instability

Context: It is thought likely that vast numbers of nanoflares are responsible for the corona having a temperature of millions of degrees. Current observational technologies lack the resolving power to confirm the nanoflare hypothesis. An alternative approach is to construct a magnetohydrodynamic coronal loop model that has the ability to predict nanoflare energy distributions. Aims: This paper presents the initial results generated by such a model. It predicts heating events with a range of sizes, depending on where the instability threshold for linear kink modes is encountered. The aims are to calculate the distribution of event energies and to investigate whether kink instability can be predicted from a single parameter. Methods: The loop is represented as a straight line-tied cylinder. The twisting caused by random photospheric motions is captured by two parameters, representing the ratio of current density to field strength for specific regions of the loop. Dissipation of the loop's magnetic energy begins during the nonlinear stage of the instability, which develops as a consequence of current sheet reconnection. After flaring, the loop evolves to the state of lowest energy where, in accordance with relaxation theory, the ratio of current to field is constant throughout the loop and helicity is conserved. Results: The results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Hence, an energy distribution of the nanoflares produced is collated. Conclusions: The final energy distribution features two nanoflare populations that follow different power laws. The power law index for the higher energy population is more than sufficient for coronal heating.Comment: 13 pages, 18 figure

On the Absence of Photospheric Net Currents in Vector Magnetograms of Sunspots Obtained From Hinode (SOT/SP)

Various theoretical and observational results have been reported regarding the presence/absence of net electric currents in the sunspots. The limited spatial resolution of the earlier observations perhaps obscured the conclusions. We have analyzed 12 sunspots observed from Hinode (SOT/SP) to clarify the issue. The azimuthal and radial components of magnetic fields and currents have been derived. The azimuthal component of the magnetic field of sunspots is found to vary in sign with azimuth. The radial component of the field also varies in magnitude with azimuth. While the latter pattern is a confirmation of the interlocking combed structure of penumbral filaments, the former pattern shows that the penumbra is made up of a "curly interlocking combed" magnetic field. The azimuthally averaged azimuthal component is seen to decline much faster than 1/$\varpi$ in the penumbra, after an initial increase in the umbra, for all the spots studied. This confirms the confinement of magnetic fields and absence of a net current for sunspots as postulated by \cite{parker96}. The existence of a global twist for a sunspot even in the absence of a net current is consistent with a fibril-bundle structure of the sunspot magnetic fields.Comment: 15 pages, 4 figures, 1 table; accepted for publication in the ApJ Letter

Current driven rotating kink mode in a plasma column with a non-line-tied free end

First experimental measurements are presented for the kink instability in a linear plasma column which is insulated from an axial boundary by finite sheath resistivity. Instability threshold below the classical Kruskal-Shafranov threshold, axially asymmetric mode structure and rotation are observed. These are accurately reproduced by a recent kink theory, which includes axial plasma flow and one end of the plasma column that is free to move due to a non-line-tied boundary condition.Comment: 4 pages, 6 figure

The Flare-energy Distributions Generated by Kink-unstable Ensembles of Zero-net-current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold

Deterministically Driven Avalanche Models of Solar Flares

We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick--slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy loading process. The model design leads to a systematic deficit of small scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.Comment: 24 pages, 11 figures, 2 tables, accepted for publication in Solar Physic

Evidence for a singularity in ideal magnetohydrodynamics: implications for fast reconnection

Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics (MHD) is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. The magnetic curvature force causes the flux rings to shrink until they come into contact. This produces a current sheet between them. In the ideal compressible calculations, the evidence for a singularity in a finite time $t_c$ is that the peak current density behaves like $|J|_\infty \sim 1/(t_c-t)$ for a range of sound speeds (or plasma betas). For the incompressible calculations consistency with the compressible calculations is noted and evidence is presented that there is convergence to a self-similar state. In the resistive reconnection calculations the magnetic helicity is nearly conserved and energy is dissipated.Comment: 4 pages, 4 figure

On the two-dimensional magnetic reconnection with nonuniform resistivity

In this paper two theoretical approaches for the calculation of the rate of quasi-stationary, two-dimensional magnetic reconnection with nonuniform anomalous resistivity are considered in the framework of incompressible magnetohydrodynamics (MHD). In the first, ``global'' equations approach the MHD equations are approximately solved for a whole reconnection layer, including the upstream and downstream regions and the layer center. In the second, ``local'' equations approach the equations are solved across the reconnection layer, including only the upstream region and the layer center. Both approaches give the same approximate answer for the reconnection rate. Our theoretical model is in agreement with the results of recent simulations of reconnection with spatially nonuniform resistivity by Baty, Priest and Forbes (2006), contrary to their conclusions.Comment: 7 pages, 1 figur

The brain recovery core: Building a system of organized stroke rehabilitation and outcomes assessment across the continuum of care

none10siThis Special Interest article describes a multidisciplinary, interinstitutional effort to build an organized system of stroke rehabilitation and outcomes measurement across the continuum of care. This system is focused on a cohort of patients who are admitted with the diagnosis of stroke to our acute facility, are discharged to inpatient and/or outpatient rehabilitation at our free-standing facility, and are then discharged to the community. This article first briefly explains the justification, goals, and purpose of the Brain Recovery Core system. The next sections describe its development and implementation, with details on the aspects related to physical therapy. The article concludes with an assessment of how the Brain Recovery Core system has changed and improved delivery of rehabilitation services. It is hoped that the contents of this article will be useful in initiating discussions and potentially facilitating similar efforts among other centers.mixedLang, Catherine E.; Bland, Marghuretta D.; Connor, Lisa Tabor; Fucetola, Robert; Whitson, Michelle; Edmiaston, Jeff; Karr, Clayton; Sturmoski, Audra; Baty, Jack; Corbetta, MaurizioLang, Catherine E.; Bland, Marghuretta D.; Connor, Lisa Tabor; Fucetola, Robert; Whitson, Michelle; Edmiaston, Jeff; Karr, Clayton; Sturmoski, Audra; Baty, Jack; Corbetta, Maurizi

The Kelvin-Helmholtz instability in weakly ionised plasmas II: multifluid effects in molecular clouds

We present a study of the Kelvin-Helmholtz instability in a weakly ionised, multifluid MHD plasma with parameters matching those of a typical molecular cloud. The instability is capable of transforming well-ordered flows into disordered flows. As a result, it may be able to convert the energy found in, for example, bowshocks from stellar jets into the turbulent energy found in molecular clouds. As these clouds are weakly ionised, the ideal magnetohydrodynamic approximation does not apply at scales of around a tenth of a parsec or less. This paper extends the work of Jones & Downes (2011) on the evolution of the Kelvin-Helmholtz instability in the presence of multifluid magnetohydrodynamic effects. These effects of ambipolar diffusion and the Hall effect are here studied together under physical parameters applicable to molecular clouds. We restrict our attention to the case of a single shear layer with a transonic, but super-Alfvenic, velocity jump and the computational domain is chosen to match the wavelength of the linearly fastest growing mode of the instability. We find that while the introduction of multifluid effects does not affect the linear growth rates of the instability, the non-linear behaviour undergoes considerable change. The magnetic field is decoupled from the bulk flow as a result of the ambipolar diffusion, which leads to a significant difference in the evolution of the field. The Hall effect would be expected to lead to a noticeable re-orientation of the magnetic field lines perpendicular to the plane. However, the results reveal that the combination with ambipolar diffusion leads to a surprisingly effective suppression of this effect.Comment: 13 pages, 13 figures, accepted for publication in MNRA