  Strongly coupled dusty plasma medium is often described as a viscoelastic
fluid that retains its memory. In a flowing dusty plasma medium, vortices of
different sizes appear when the flow does not remain laminar. The vortices also
merge to transfer energy between different scales. In the present work, we
study the effect of viscoelasticity and compressibility over a localized vortex
structure and multiple rotational vortexes in a strongly coupled viscoelastic
dusty plasma medium. In case of single rotating vortex flow, a transverse wave
is generated from the localized vortex source and the evolution time of
generated waves is found to be reduced due to finite viscoelasticity and
compressibility of the medium. It is found that the viscoelasticity suppresses
the dispersion of vorticity. In the presence of multiple vortices, we find, the
vortex mergers get highly affected in the presence of memory effect of the
fluid, and thus the dynamics of the medium gets completely altered compared to
a non-viscoelastic fluid. For a compressible fluid, viscoelasticity damps out
the energy in the sonic waves generated in the medium. Thus a highly
viscoelastic and compressible fluid, in some cases, behaves similarly to an
incompressible viscoelastic fluid. The wave-front like rings propagate in
elliptical orbits keeping the footprint of the earlier position of the
point-vortex. The rings collide with each other even within the patch vortex
region forming regions of high vorticity at the point of intersection and pass
through each other.
