The Geometry of Reconnection

Abstract

Reconnection is an important process of structure formation in fluid dynamics. It occurs in the form of vortex reconnection in hydrodynamics as well as in the form of magnetic reconnection in plasmas. In both cases a divergence-free field, the magnetic or the vorticity field, respectively, alter the topology of their field lines. A first definition of the process in two dimensions is given, which is wide enough to cover both forms of reconnection, and which is independent of the underlying dissipation process. It is also demonstrated that the definition can distinguish reconnection from other non-ideal processes. With the help of simple two-dimensional examples, one for magnetic reconnection and one for vortex reconnection, similarities and differences of both types of reconnection are discussed. The transition to three-dimensional configurations shows to require a more general framework, which is found in the covariant generalization of flux conservation.