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Through a direct comparison between numerical simulations in two and threedimensions, we investigate topological effects in reconnection. A simpleestimate on increase in reconnection rate in three dimensions by a factor of$\sqrt{2}$, when compared with a two-dimensional case, is confirmed in oursimulations. We also show that both the reconnection rate and the fraction ofmagnetic energy in the simulations depend linearly on the height of thereconnection region. The degree of structural complexity of a magnetic fieldand the underlying flow is measured by current helicity and cross-helicity. Wecompare results in simulations with different computational box heights.

Magnetic reconnection in a comparison of topology and helicities in two and three dimensional resistive MHD simulations