We consider a special configuration of vorticity that consists of a pair of
externally tangent circular vortex sheets, each having a circularly symmetric core
of bounded vorticity concentric to the sheet, and each core precisely balancing the
vorticity mass of the sheet. This configuration is a stationary weak solution of the
2D incompressible Euler equations. We propose to perform numerical experiments to verify
that certain approximations of this flow configuration converge to a non-stationary
weak solution. Preliminary simulations presented here suggest this is
indeed the case. We establish a convergence theorem for the vortex blob method that
applies to this problem. This theorem and the preliminary calculations we carried out
support the existence of two distinct weak solutions with the same initial data.