The vortex blob method as a second-grade non-Newtonian fluid

We show that a certain class of vortex blob approximations for ideal hydrod ynamics in two dimensions can be rigorously understood as solutions to the equations of second-grade non-Newtonian fluids with zero viscosity and init ial data in the space of Radon measures M(R-2). The solutions of this regul arized PDE, also known as the isotropic Lagrangian averaged Euler or Euler- cr equations, are geodesics on the volume preserving diffeomorphism group w ith respect to a new weak right invariant metric. We prove global existence of unique weak solutions (geodesics) for initial vorticity in M(R-2) such as point-vortex data, and show that the associated coadjoint orbit is prese rved by the flow. Moreover, solutions of this particular vortex blob method converge to solutions of the Euler equations with bounded initial vorticit y, provided that the initial data is approximated weakly in measure, and th e total variation of the approximation also converges. In particular, this includes grid-based approximation schemes as are common in practical vortex computations.