Geophys. Astrophys. Fluid Dynamics 106 (2012) 701-709.

Formation of magnetic flux tubes in cylindrical wedge geometry

G.J.J. Botha(1), A.M.Rucklidge(2) and N.E. Hurlburt(3)
(1) Department of Physics,
University of Warwick, Coventry CV4 7AL, UK

(2) Department of Applied Mathematics,
University of Leeds, Leeds LS2 9JT, UK

(3) Lockheed Martin Solar and Astrophysics Laboratory,
Organization L9-41 Building 252, Palo Alto, CA 94304, USA

Abstract. Three-dimensional (3D) magnetohydrodynamic (MHD) numerical simulations have not been able to demonstrate convincingly the spontaneous formation of large vertical, i.e., pore-like or sunspot-like, flux tubes. Two-dimensional (2D) magnetoconvection in axisymmetric cylinders forms a central magnetic flux tube surrounded by annular convection rings. To study the robustness of this type of solution in three dimensions, the nonlinear resistive MHD equations are solved numerically in a 3D cylindrical wedge from an initially uniform vertical magnetic field. It is shown that the 2D result is retrieved for small domain radii. However, for larger radii the central axis loses its importance and in this case many convection cells form in the numerical domain. Magnetic flux is captured between cells where flow converges and the reduced amount of flux that congregates at the central axis is eroded by the surrounding convection.

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