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Register a new userMagnetic helicity dissipation and production in an ideal MHD code
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We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales. As a consequence, the small-scale current helicity is too small compared with that of the DNS. The resulting net current helicity has then always the wrong sign, and its statistical average also does not approach zero at late times, as expected from the DNS. Our results have implications for astrophysical dynamo simulations of stellar and galactic magnetism using ideal MHD codes.
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We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic turbulence for helicity injection at a scale that is much smaller than the scale of energy injection. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in a domain with a high level of relative magnetic helicity, which determines that part of the magnetic energy related to the helical modes at a given scale. If the relative helicity approaches unity, the spectral slope tends to $-3/2$. We show that this energy pileup is caused by an inverse cascade of magnetic energy associated with the magnetic helicity. This negative energy flux is the contribution of the pure magnetic-to-magnetic energy transfer, which vanishes in the non-helical limit. In the context of astrophysical dynamos, our results indicate that a large-scale dynamo can be affected by the magnetic helicity generated at small scales. The kinetic helicity, in particular, is not involved in the process at all. An interesting finding is that an inverse cascade of magnetic energy can be provided by a small-scale source of magnetic helicity fluctuations without a mean injection of magnetic helicity.
Magnetic helicity is robustly conserved in systems with large magnetic Reynolds numbers, including most systems of astrophysical interest. This plays a major role in suppressing the kinematic large scale dynamo and driving the large scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. Errors in the internal distribution of magnetic helicity are equally serious and possibly larger. Here we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations.
We study the propagation and dissipation of magnetohydrodynamic waves in a set of numerical models that each include a solar--like stratified atmosphere and a magnetic field with a null point. All simulations have the same magnetic field configuration but different transition region heights. Compressive wave packets introduced in the photospheric portion of the simulations refract towards the null and collapse it into a current sheet, which then undergoes reconnection. The collapsed null forms a current sheet due to a strong magnetic pressure gradient caused by the inability of magnetic perturbations to cross the null. Although the null current sheet undergoes multiple reconnection episodes due to repeated reflections off the lower boundary, we find no evidence of oscillatory reconnection arising from the dynamics of the null itself. Wave mode conversion around the null generates a series of slow mode shocks localized near each separatrix. The shock strength is asymmetric across each separatrix, and subsequent shock damping therefore creates a tangential discontinuity across each separatrix, with long--lived current densities. A parameter study of the injected wave energy to reach the null confirms our previous WKB estimates. Finally, using current estimates of the photospheric acoustic power, we estimate that the shock and Ohmic heating we describe may account for $approx1-10%$ of the radiative losses from coronal bright points with similar topologies, and are similarly insufficient to account for losses from larger structures such as ephemeral regions. At the same time, the dynamics are comparable to proposed mechanisms for generating type--II spicules.
Turbulent properties of the quiet Sun represent the basic state of surface conditions, and a background for various processes of solar activity. Therefore understanding of properties and dynamics of this `basic state is important for investigation of more complex phenomena, formation and development of observed phenomena in the photosphere and atmosphere. For characterization of the turbulent properties we compare kinetic energy spectra on granular and sub-granular scales obtained from infrared TiO observations with the New Solar Telescope (Big Bear Solar Observatory) and from 3D radiative MHD numerical simulations (SolarBox code). We find that the numerical simulations require a high spatial resolution with 10 - 25 km grid-step in order to reproduce the inertial (Kolmogorov) turbulence range. The observational data require an averaging procedure to remove noise and potential instrumental artifacts. The resulting kinetic energy spectra show a good agreement between the simulations and observations, opening new perspectives for detailed joint analysis of more complex turbulent phenomena on the Sun, and possibly on other stars. In addition, using the simulations and observations we investigate effects of background magnetic field, which is concentrated in self-organized complicated structures in intergranular lanes, and find an increase of the small-scale turbulence energy and its decrease at larger scales due to magnetic field effects.
A method for implementing cylindrical coordinates in the Athena magnetohydrodynamics (MHD) code is described. The extension follows the approach of Athenas original developers and has been designed to alter the existing Cartesian-coordinates code as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport, a central feature of the Athena algorithm, while making use of previously implemented code modules such as the Riemann solvers. Angular-momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully. We describe modifications for cylindrical coordinates of the higher-order spatial reconstruction and characteristic evolution steps as well as the finite-volume and constrained transport updates. Finally, we present a test suite of standard and novel problems in one-, two-, and three-dimensions designed to validate our algorithms and implementation and to be of use to other code developers. The code is suitable for use in a wide variety of astrophysical applications and is freely available for download on the web.
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