  We consider a sequence of Leray-Hopf weak solutions of the 2D Navier-Stokes
equations on a bounded domain, in the vanishing viscosity limit. We provide
sufficient conditions on the associated vorticity measures, away from the
boundary, which ensure that as the viscosity vanishes the sequence converges to
a weak solution of the Euler equations. These assumptions are consistent with
vortex sheet solutions of the Euler equations.
