  It is well-known that the dynamics of vortices in an ideal incompressible
two-dimensional fluid contained in a bounded not necessarily simply connected
smooth domain is described by the Kirchhoff--Routh point vortex system. In this
paper, we revisit the classical problem of how well solutions to the Euler
equations approximate these vortex dynamics and extend previous rigorous
results to the case where the vorticity field is unbounded. More precisely, we
establish estimates for the $2$-Wasserstein distance between the vorticity and
the empirical measure associated with the point vortex dynamics. In particular,
we derive an estimate on the order of weak convergence of the Euler solutions
to the solutions of the point vortex system.
