R. B. Dahlburg

Reconnection of Twisted Flux Tubes as a Function of Contact Angle

The collision and reconnection of magnetic flux tubes in the solar corona has been proposed as a mechanism for solar flares and in some cases as a model for coronal mass ejections. We study this process by simulating the collision of pairs of twisted flux tubes with a massively parallel, collocation, viscoresistive, magnetohydrodynamic code using up to 256 × 256 × 256 Fourier modes. Our aim is to investigate the energy release and possible global topological changes that can occur in flux-tube reconnection. We have performed a number of simulations for different angles between the colliding flux tubes and for either co- or counterhelicity flux tubes. We find the following four classes of interaction: (1) bounce (no appreciable reconnection), (2) merge, (3) slingshot (the most efficient reconnection), and (4) tunnel (a double reconnection). We will describe these four classes of flux-tube reconnection and discuss in what range of parameter space each class occurs and the implications our results have for models of flares and coronal mass ejections.

Direct and large-eddy simulations of three-dimensional compressible Navier-Stokes turbulence

This paper reports results from the numerical implementation and testing of the compressible large‐eddy simulation (LES) model described by Speziale et al. [Phys. Fluids 31, 940 (1988)] and Erlebacher et al. (to appear in J. Fluid Mech.). Relevant quantities from 323 ‘‘coarse grid’’ LES solutions are compared with results generated from 963 direct numerical simulations (DNS) of three‐dimensional compressible turbulence. It is found that the 323 LES results overall agree well with their 963 DNS counterparts. Moreover, the new DNS results confirm several recent conclusions about compressible turbulence that have been based primarily on two‐dimensional simulations.

Evolution of the Orszag–Tang vortex system in a compressible medium. I. Initial average subsonic flow

In this paper the results of fully compressible, Fourier collocation, numerical simulations of the Orszag–Tang vortex system are presented. The initial conditions for this system consist of a nonrandom, periodic field in which the magnetic and velocity field contain X points but differ in modal structure along one spatial direction. The velocity field is initially solenoidal, with the total initial pressure field consisting of the superposition of the appropriate incompressible pressure distribution upon a flat pressure field corresponding to the initial, average Mach number of the flow. In these numerical simulations, this initial Mach number is varied from 0.2–0.6. These values correspond to average plasma beta values ranging from 30.0 to 3.3, respectively. It is found that compressible effects develop within one or two Alfven transit times, as manifested in the spectra of compressible quantities such as the mass density and the nonsolenoidal flow field. These effects include (1) a retardation of growth...

Coronal Heating, Weak MHD Turbulence, and Scaling Laws

Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B0, which depends on the spectral index of total energy for given loop parameters, must vary from B for weak fields to B for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.

Evolution of the Orszag--Tang vortex system in a compressible medium. II. Supersonic flow

The numerical investigation of Orszag–Tang vortex system in compressible magnetofluids continues, this time using initial conditions with embedded supersonic regions. The simulations have initial average Mach numbers M=1.0 and 1.5 and β=10/3 with Lundquist numbers S=50, 100, or 200. Depending on the particular set of parameters, the numerical grid contains 2562 or 5122 collocation points. The behavior of the system differs significantly from that found previously for the incompressible and subsonic analogs. Shocks form at the downstream boundaries of the embedded supersonic regions outside the central magnetic X point and produce strong local current sheets that dissipate appreciable magnetic energy. Reconnection at the central X point, which dominates the incompressible and subsonic systems, peaks later and has a smaller impact as M increases from 0.6 to 1.5. Reconnection becomes significant only after shocks reach the central region, compressing the weak current sheet there. Similarly, the correlation b...

Formation of the slow solar wind in a coronal streamer

We have investigated a magnetohydrodynamic mechanism that accounts for several fundamental properties of the slow solar wind, in particular its variability, latitudinal extent, and bulk acceleration. In view of the well-established association between the streamer belt and the slow wind, our model begins with a simplified representation of a streamer beyond the underlying coronal helmet: a neutral sheet embedded in a plane fluid wake. This wake-neutral sheet configuration is characterized by two parameters that vary with distance from the Sun: the ratio of the cross-stream velocity scale to the neutral sheet width, and the ratio of the typical Alfven velocity to the typical flow speed far from the neutral sheet. Depending on the values of these parameters, our linear theory predicts that three kinds of instability can develop when this system is perturbed: a tearing instability and two ideal fluid instabilities with different cross-stream symmetries (varicose and sinuous). In the innermost, magnetically dominated region beyond the helmet cusp, we find that the streamer is resistively and ideally unstable, evolving from tearing-type reconnection in the linear regime to a nonlinear varicose fluid instability. Traveling magnetic islands are formed which are similar to features recently revealed by the large-angle spectroscopic coronagraph on the joint European Space Agency/NASA Solar and Heliospheric Observatory (SOHO) [Brueckner et al., 1995]. During this process, the center of the wake is accelerated and broadened slightly. Past the Alfven point, where the kinetic energy exceeds the magnetic energy, the tearing mode is suppressed, but an ideal sinuous fluid mode can develop, producing additional acceleration up to typical slow wind speeds and substantial broadening of the wake. Farther from the Sun, the system becomes highly turbulent as a result of the development of ideal secondary instabilities, thus halting the acceleration and producing strong filamentation throughout the core of the wake. We discuss the implications of this model for the origin and evolution of the slow solar wind, and compare the predicted properties with current observations from SOHO.

Secondary instability in three-dimensional magnetic reconnection

The transition to turbulence in three‐dimensional reconnection of a magnetic neutral sheet is investigated. The transition can occur via a three‐step process. First, the sheet undergoes the usual tearing instability. Second, the tearing mode saturates to form a two‐dimensional quasisteady state. Third, this secondary equilibrium is itself ideally unstable when it is perturbed by three‐dimensional disturbances. Most of this paper is devoted to the analysis and simulation of the three‐dimensional linear stability properties of the two‐dimensional saturated tearing layer. The numerical simulations are performed with a semi‐implicit, pseudospectral‐Fourier collocation algorithm. A three‐dimensional secondary linear instability that grows on the ideal time scale is identified. An examination of the modal energetics reveals that the largest energy transfer is from the mean field to the three‐dimensional field, with the two‐dimensional field acting as a catalyst. Results of some high‐resolution, fully nonlinear ...

Nonlinear Evolution of Kink-unstable Magnetic Flux Tubes and Solar δ-Spot Active Regions

The motivation for the work described in this paper is to understand kink-unstable magnetic flux tubes and their role in the formation of δ-spot active regions. It has been proposed that, during their rise to the photosphere, a certain fraction of convection zone flux tubes become twisted to the point where they are unstable to the current driven kink instability. These kink-unstable flux tubes then evolve toward a new, kinked equilibrium as they continue to rise to the photosphere, appearing as δ-spot groups upon emergence. Because of their kinked nature, these flux tubes could be highly susceptible to flaring, explaining the very active nature of δ-spot groups. We study the kinking flux tube problem with a three-dimensional numerical model containing only the most basic features of a kink-unstable flux tube. We build on our earlier work describing the linear phase of the kink instability, and follow the evolution into the nonlinear regime: (1) We perform numerical simulations of constant-twist, kink-unstable flux tubes in an initially cylindrical equilibrium configuration in three dimensions, in a high-β pressure-confined environment. We consider many different initial configurations, including the Gold-Hoyle flux tube. (2) These numerical calculations confirm the growth-rate predictions of our earlier work, when viscous dissipation is included. They also confirm our velocity profile predictions. (3) The flux tubes evolve toward new helically symmetric equilibrium configurations. (4) The timescale for saturation to the kinked equilibrium configuration is τsat ~ 10/ω0, where ω0 is the linear growth rate calculated as in the earlier paper. (5) The cylindrically symmetric part of the kinked equilibrium is well described by the m = 0 Chandrasekhar-Kendall functions (i.e., the Lundquist field). The m = 1 helically symmetric part, however, is not well described by the m = 1 Chandrasekhar-Kendall functions. (6) The equilibrium kink amplitudes are not large, at less than one-third of the tube radius. (7) The peak kinetic energy of the instability can be predicted from the initial excess perpendicular magnetic energy. (8) The amplitudes of the kinked tubes are large enough to give a δ-spot region tilt angle of up to 30° away from that of an unkinked tube.

Plasmoid Formation and Acceleration in the Solar Streamer Belt

The dynamical behavior of a configuration consisting of a plane fluid wake flowing in a current sheet embedded in a plasma sheet that is denser than its surroundings is discussed. This configuration is a useful model for a number of structures of astrophysical interest, such as solar coronal streamers, cometary tails, the Earths magnetotail and Galactic center nonthermal filaments. In this paper, the results are applied to the study of the formation and initial motion of the plasma density enhancements observed by the Large-Angle Spectrometric Coronagraph (LASCO) instrument onboard the Solar and Heliospheric Observatory (SOHO) spacecraft. It is found that beyond the helmet cusp of a coronal streamer, the magnetized wake configuration is resistively unstable, that a traveling magnetic island develops at the center of the streamer, and that density enhancements occur within the magnetic islands. As the massive magnetic island travels outward, both its speed and width increase. The island passively traces the acceleration of the inner part of the wake. The values of the acceleration and density contrasts are in good agreement with LASCO observations.

Drift wave instability in the Helimak experiment

Electrostatic drift wave linear stability analysis is carried out for the Helimak configuration and compared against experimental data. Density fluctuation and cross-spectrum measurements show evidence of a coherent mode propagating perpendicular to the magnetic field which becomes unstable at k⊥ρs∼0.15. By comparing the experimental results with the wave characteristic of linear two-fluid theory, this mode is identified as an unstable resistive drift wave driven by the density gradient and magnetic grad-B/curvature present in an otherwise magnetohydrodynamic stable steady-state equilibrium.