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Register a new userMagnetic suppression of zonal flows on a beta plane
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Zonal flows in rotating systems have been previously shown to be suppressed by the imposition of a background magnetic field aligned with the direction of rotation. Understanding the physics behind the suppression may be important in systems found in astrophysical fluid dynamics, such as stellar interiors. However, the mechanism of suppression has not yet been explained. In the idealized setting of a magnetized beta plane, we provide a theoretical explanation that shows how magnetic fluctuations directly counteract the growth of weak zonal flows. Two distinct calculations yield consistent conclusions. The first, which is simpler and more physically transparent, extends the Kelvin-Orr shearing wave to include magnetic fields and shows that weak, long-wavelength shear flow organizes magnetic fluctuations to absorb energy from the mean flow. The second calculation, based on the quasilinear, statistical CE2 framework, is valid for arbitrary wavelength zonal flow and predicts a self-consistent growth rate of the zonal flow. We find that a background magnetic field suppresses zonal flow if the bare Alfven frequency is comparable to or larger than the bare Rossby frequency. However, suppression can occur for even smaller magnetic fields if the resistivity is sufficiently small enough to allow sizable magnetic fluctuations. Our calculations reproduce the $eta/B_0^2 = text{const.}$ scaling that describes the boundary of zonation, as found in previous work, and we explicitly link this scaling to the amplitude of magnetic fluctuations.
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Aims. We show how the build-up of magnetic gradients in the Suns corona may be inferred directly from photospheric velocity data. This enables computation of magnetic connectivity measures such as the squashing factor without recourse to magnetic field extrapolation. Methods.Assuming an ideal evolution in the corona, and an initially uniform magnetic field, the subsequent field line mapping is computed by integrating trajectories of the (time-dependent) horizontal photospheric velocity field. The method is applied to a 12 hour high-resolution sequence of photospheric flows derived from Hinode/SOT magnetograms. Results. We find the generation of a network of quasi-separatrix layers in the magnetic field, which correspond to Lagrangian coherent structures in the photospheric velocity. The visual pattern of these structures arises primarily from the diverging part of the photospheric flow, hiding the effect of the rotational flow component: this is demonstrated by a simple analytical model of photospheric convection. We separate the diverging and rotational components from the observed flow and show qualitative agreement with purely diverging and rotational models respectively. Increasing the flow speeds in the model suggests that our observational results are likely to give a lower bound for the rate at which magnetic gradients are built up by real photospheric flows. Finally, we construct a hypothetical magnetic field with the inferred topology, that can be used for future investigations of reconnection and energy release.
In this paper we seek to understand the timescale on which the photospheric motions on the Sun braid coronal magnetic field lines. This is a crucial ingredient for determining the viability of the braiding mechanism for explaining the high temperatures observed in the corona. We study the topological complexity induced in the coronal magnetic field, primarily using plasma motions extracted from magneto-convection simulations. This topological complexity is quantified using the field line winding, finite time topological entropy and passive scalar mixing. With these measures we contrast mixing efficiencies of the magneto-convection simulation, a benchmark flow known as a ``blinking vortex, and finally photospheric flows inferred from sequences of observed magnetograms using local correlation tracking. While the highly resolved magneto-convection simulations induce a strong degree of field line winding and finite time topological entropy, the values obtained from the observations from the plage region are around an order of magnitude smaller. This behavior is carried over to the finite time topological entropy. Nevertheless, the results suggest that the photospheric motions induce complex tangling of the coronal field on a timescale of hours.
By defining an appropriate field line helicity, we apply the powerful concept of magnetic helicity to the problem of global magnetic field evolution in the Suns corona. As an ideal-magnetohydrodynamic invariant, the field line helicity is a meaningful measure of how magnetic helicity is distributed within the coronal volume. It may be interpreted, for each magnetic field line, as a magnetic flux linking with that field line. Using magneto-frictional simulations, we investigate how field line helicity evolves in the non-potential corona as a result of shearing by large-scale motions on the solar surface. On open magnetic field lines, the helicity injected by the Sun is largely output to the solar wind, provided that the coronal relaxation is sufficiently fast. But on closed magnetic field lines, helicity is able to build up. We find that the field line helicity is non-uniformly distributed, and is highly concentrated in twisted magnetic flux ropes. Eruption of these flux ropes is shown to lead to sudden bursts of helicity output, in contrast to the steady flux along the open magnetic field lines.
This work examines the effect of the embedded magnetic field strength on the non-linear development of the magnetic Rayleigh-Taylor Instability (RTI) (with a field-aligned interface) in an ideal gas close to the incompressible limit in three dimensions. Numerical experiments are conducted in a domain sufficiently large so as to allow the predicted critical modes to develop in a physically realistic manner. The ratio between gravity, which drives the instability in this case (as well as in several of the corresponding observations), and magnetic field strength is taken up to a ratio which accurately reflects that of observed astrophysical plasma, in order to allow comparison between the results of the simulations and the observational data which served as inspiration for this work. This study finds reduced non-linear growth of the rising bubbles of the RTI for stronger magnetic fields, and that this is directly due to the change in magnetic field strength, rather than the indirect effect of altering characteristic length scales with respect to domain size. By examining the growth of the falling spikes, the growth rate appears to be enhanced for the strongest magnetic field strengths, suggesting that rather than affecting the development of the system as a whole, increased magnetic field strengths in fact introduce an asymmetry to the system. Further investigation of this effect also revealed that the greater this asymmetry, the less efficiently the gravitational energy is released. By better understanding the under-studied regime of such a major phenomenon in astrophysics, deeper explanations for observations may be sought, and this work illustrates that the strength of magnetic fields in astrophysical plasmas influences observed RTI in subtle and complex ways.
In this study we investigate the effects of turbulent convection on formation of large-scale inhomogeneous magnetic structures by means of Large-Eddy Simulation (LES) for convection in solar-type stars. The main idea of this study is the implementation of a new subgrid-scale model for the effective Lorentz force in a three-dimensional nonlinear radiative magnetohydrodynamics (MHD) code developed for simulating the upper solar convection zone and lower atmosphere. To this end we derived the energy budget equations, which include the effects of the subgrid-scale turbulence on the Lorentz-force, and implemented the new subgrid-scale turbulence model (TELF-Model) in a three-dimensional nonlinear MHD LES code. Using imposed initial vertical and horizontal uniform magnetic fields in LES with the TELF-Model, we have shown that the magnetic flux tubes formation is started when the initial mean magnetic field is larger than a threshold value (about 100 G). This is in agreement with the theoretical studies by Rogachevskii and Kleeorin (2007). We have determined the vertical profiles of the velocity and magnetic fluctuations, total MHD energy and anisotropy of turbulent magneto-convection, kinetic and current and cross helicities.
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