Effect of In-Plane Shear Flow on the Magnetic Island Coalescence Instability

Using a 2D Viscoresistive Reduced MagnetoHydroDynamic (VR-RMHD) 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 [33] and Throumoulopoulos et al [34] in the sub-Alfv\'enic flow shear regime for Fadeev equilibrium, the super-Alfv\'enic 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-Alfv\'enic and super-Alfv\'enic 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-Alfv\'enic to super- Alfv\'enic flow speeds. For scale lengths smaller than the island size, the reconnection rate decreases upto a critical value $v_{0c}$, beyond which, the shear flow is found to destabilize the islands. The value of v0c decreases with 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-Alfv\'enic 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 decrease in upstream velocity, causing less pile-up of magnetic flux on both sides of the reconnection sheet.