We prove the convergence of a discontinuous Galerkin method approximating
the 2-D incompressible Euler equations with discontinuous initial vorticity:$omega_0 in
L^2(Omega)$. Furthermore, when $omega_0 in L^infty(Omega)$, the whole sequence is shown to be
strongly convergent. This is the first convergence result in numerical approximations
of this general class of discontinuous flows. Some important flows such as
vortex patches belong to this class.