  We study the effects of turbulence on magnetic reconnection using 3D
numerical simulations. This is the first attempt to test a model of fast
magnetic reconnection in the presence of weak turbulence proposed by Lazarian &
Vishniac (1999). This model predicts that weak turbulence, generically present
in most of astrophysical systems, enhances the rate of reconnection by reducing
the transverse scale for reconnection events and by allowing many independent
flux reconnection events to occur simultaneously. As a result the reconnection
speed becomes independent of Ohmic resistivity and is determined by the
magnetic field wandering induced by turbulence. To quantify the reconnection
speed we use both an intuitive definition, i.e. the speed of the reconnected
flux inflow, as well as a more sophisticated definition based on a formally
derived analytical expression. Our results confirm the predictions of the
Lazarian & Vishniac model. In particular, we find that Vrec Pinj^(1/2), as
predicted by the model. The dependence on the injection scale for some of our
models is a bit weaker than expected, i.e. l^(3/4), compared to the predicted
linear dependence on the injection scale, which may require some refinement of
the model or may be due to the effects like finite size of the excitation
region. The reconnection speed was found to depend on the expected rate of
magnetic field wandering and not on the magnitude of the guide field. In our
models, we see no dependence on the guide field when its strength is comparable
to the reconnected component. More importantly, while in the absence of
turbulence we successfully reproduce the Sweet-Parker scaling of reconnection,
in the presence of turbulence we do not observe any dependence on Ohmic
resistivity, confirming that our reconnection is fast.
