Abstract
Reconnection is an important process of structure formation in fluid dynamics, occurring in the form of vortex reconnection in hydrodynamics as well as in the form of magnetic reconnection in plasmas. There is a close analogy between the quantities involved in both phenomena but, surprisingly, the process of magnetic reconnection, although complicated by the presence of a magnetic field, is geometrically simpler than vortex reconnection; it may thus serve as good starting point to understand the geometry of vortex reconnection.
A general covariant definition of reconnection is given and, starting from a simple analytic model of magnetic reconnection, the basic process of reconnection is analyzed. The model is then modified to meet the additional constraints of vortex reconnection. It is shown that, although the evolution of the vorticity near the reconnection site is stationary and two-dimensional the flow velocity is inevitably three-dimensional, and time dependent. Explicit expressions for the reconnected flux and the reconnection time are given.
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© 2001 Springer-Verlag Berlin Heidelberg
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Hornig, G. (2001). The Geometry of Magnetic and Vortex Reconnection. In: Barenghi, C.F., Donnelly, R.J., Vinen, W.F. (eds) Quantized Vortex Dynamics and Superfluid Turbulence. Lecture Notes in Physics, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45542-6_37
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DOI: https://doi.org/10.1007/3-540-45542-6_37
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