  This work is a numerical study of the two-dimensional merging phenomena
between two Lamb-Oseen co-rotating vortices in a viscoelastic fluid. We use a
generalized hydrodynamics fluid model to study vortex merging in a strongly
coupled dusty plasma medium, which exhibits characteristics similar to a
viscoelastic fluid. Several aspects influencing the merging phenomena are
considered: the aspect ratio (core size/separation distance), the relative
circulation strengths of each vortex, and the coupling strength of the medium.
Unlike classical hydrodynamic fluids, we find that for viscoelastic fluids,
shear waves facilitate the merging events even for widely separated vortices.
The merging process is accelerated in media with higher coupling strengths, but
the resultant vortex shape decays more quickly as well. It is also found that
varying either the vortex scale or the vortex circulation strength can result
in a similar merging process, where a smaller (larger) vortex acts like a
vortex with weaker (stronger) circulation. Finally, we show that a
Poynting-like conservation theorem is satisfied for the examined merging
processes.
