Clamshell and Tipping Instabilities in a Two‐dimensional Magnetohydrodynamic Tachocline

Abstract

Building on Cally's nonlinear model of two-dimensional MHD tachocline instability, we further explore the evolution of a wide variety of toroidal field profiles due to this instability. Cally showed in a recent study that an initially broad toroidal field opens up into a ``clamshell'' pattern because of nonlinear evolution of MHD tachocline instability. Various other toroidal field profiles-single toroidal bands, double bands, and mixed profiles with a band in addition to broad profiles-may also occur in the Sun during various phases of the solar cycle. Detailed study of the evolution of banded profiles shows no occurrence of clamshell instability, but the bands commonly tip relative to the axis of rotation. The higher the latitude location of the band, the more it tips. Extreme tipping results when the band is at 60° latitude or higher-the magnetic ring hangs from the pole on one side of the Sun. For bands of 10° latitude width at sunspot latitudes ( 15°) in latitude, as well as two close bands of same polarities, do not interact in the same hemisphere-the higher latitude band tips, while the lower latitude band hardly responds. A significant interaction between two individual bands in one hemisphere takes place only when the band separation is