A FAMILY OF 2-DIMENSIONAL NONLINEAR SOLUTIONS FOR MAGNETIC-FIELD ANNIHILATION

We present a family of nonlinear solutions for magnetic field annihilation in two dimensions. These solutions include fully the effects of viscosity and resistivity and are a generalization of the Sonnerup and Priest model, where an irrotational stagnation point flow carries straight field lines toward a long, thin current sheet. Here, we allow for vorticity in the inflow. When this is low, there is a unique solution for the flow and magnetic field. The current sheet adjusts its dimensions to accommodate different inflows. It is widest for a negative imposed vorticity and increases in width as the resistivity or viscosity is increased. When the imposed vorticity is large and negative, however, the solutions become nonunique, the flow pattern becomes cellular, and current sheets develop at the cell boundaries. These results, then, show that it is possible to have many more different types of inflow matched to full solutions for the current sheet than have been considered hitherto.