  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.
