Effect of in-plane shear flow on the magnetic island coalescence instability

Abstract

Using a 2D Viscoresistive Reduced MagnetoHydroDynamic model, the magnetic island coalescence problem is studied in the presence of in-plane, parallel shear flows. Extending the analytical work of Waelbroeck et al. [Phys. Plasmas 14, 022302 (2007)] and Throumoulopoulos et al., [J. Phys. A 42, 335501 (2009)] in the sub-Alfvénic flow shear regime for Fadeev equilibrium, the super-Alfvénic regime is studied for the first time numerically. A wide range of values of shear flow amplitudes and shear scale lengths have been considered to understand the effect of sub-Alfvénic and super-Alfvénic flows on the coalescence instability and its nonlinear fate. We find that for flow shear length scales greater than the magnetic island size, the maximum reconnection rate decreases monotonically from sub-Alfvénic to super-Alfvénic flow speeds. For scale lengths smaller than the island size, the reconnection rate decreases up to a critical value v0c, beyond which the shear flow is found to destabilize the islands. The value of v0c decreases with a decrease in the value of shear flow length scale. Interestingly, for our range of parameters, we find suppression of the Kelvin–Helmholtz instability in super-Alfvénic flows even when the shear scale length is smaller than the island width. Observation of velocity streamlines shows that the plasma circulation inside the islands has a stabilizing influence in strong shear flow cases. Plasma circulation is also found to be responsible for the decrease in upstream velocity, causing less pileup of magnetic flux on both sides of the reconnection sheet.