Time-dependent magnetic reconnection in two-dimensional periodic geometry

We compare the predictions of incompressible, analytic reconnection theory with numerical simulations performed using a time-dependent, doubly periodi c code. The properties of the simulated current sheets are shown to be in g ood quantitative agreement with recent planar analytic reconnection solutio ns based on X-point merging driven by sheared incompressible flows. We conc lude that the analytic treatment is not seriously compromised by assuming a n open flow geometry and a one-dimensional current layer. The analytic mode ls, when augmented by nonlinear saturation arguments, are also shown to pro vide resistive scaling laws that accord well with computed merging rates. B y way of contrast, we have found no computational evidence for the osculati on of separatrices in current sheets, even for the case of classical head-o n reconnection in which all shearing flows are absent. We attribute this to the dynamic nature of the simulated current sheet. Our simulations provide some evidence that dynamic current sheets can break up into magnetic islan ds, but whether this fragmentation can be attributed to the tearing mode in stability remains unclear.