Two-dimensional simulations of buoyantly rising, interacting magnetic flux tubes

We perform two-dimensional simulations of the buoyant rise of twisted horizontal magnetic flux tubes through an adiabatically stratified layer representing the solar convection zone or other marginally stable atmosphere. The numerical calculations employ the anelastic approximation to the basic MI-ID equations. We confirm the results of recent compressible simulations by Moreno-Insertis & Emonet that the azimuthal component of the tube magnetic field can prevent the splitting of the tube into a vortex pair, and that most of the flux in the initial tube cross section rises in the form of a rigid body that reaches a terminal speed similar to the prediction of the often-employed thin-flux-tube model. We also study the interaction between a pair of buoyant flux tubes as they rise in proximity. In the case of two identical flux tubes that start from the same level, we iind that the wake behind each tube interacts with the wake of the other; prompting mirror-symmetric vortex shedding in each wake. As a result, each tube gains around it a net circulation of the opposite sign of the most recently shed eddy; this causes a periodic, horizontal lift force that makes the tubes oscillate horizontally as they rise. The tube interactions in this case differ substantially from the inviscid limit studied previously. For two identical flux tubes that start at different levels, the resulting interactions depend upon the details of the initial configuration of the two tubes and can be very different from the interactions seen in the symmetrical case. In the asymmetric case, it becomes possible for one flux tube to be drawn into the wake of the other, leading eventually to a merger of the tubes.