  We establish the inviscid limit of the incompressible Navier-Stokes equations
on the whole plane $\mathbb{R}^2$ for initial data having vorticity as a
superposition of point vortices and a regular component. In particular, this
rigorously justifies the vortex-wave system from the physical Navier-Stokes
flows in the vanishing viscosity limit, a model that was introduced by
Marchioro and Pulvirenti in the early 90s to describe the dynamics of point
vortices in a regular ambient vorticity background. The proof rests on the
previous analysis of Gallay in his derivation of the vortex-point system.
