  We show that a certain class of vortex blob approximations for ideal
hydrodynamics in two dimensions can be rigorously understood as solutions to
the equations of second-grade non-Newtonian fluids with zero viscosity, and
initial data in the space of Radon measures ${\mathcal M}({\mathbb R}^2)$. The
solutions of this regularized PDE, also known as the averaged Euler or
Euler-$\alpha$ equations, are geodesics on the volume preserving diffeomorphism
group with respect to a new weak right invariant metric. We prove global
existence of unique weak solutions (geodesics) for initial vorticity in
${\mathcal M}({\mathbb R}^2)$ such as point-vortex data, and show that the
associated coadjoint orbit is preserved by the flow. Moreover, solutions of
this particular vortex blob method converge to solutions of the Euler equations
with bounded initial vorticity, provided that the initial data is approximated
weakly in measure, and the total variation of the approximation also converges.
In particular, this includes grid-based approximation schemes of the type that
are usually used for vortex methods.
