  We use recent developments in the theory of finite-time dynamical systems to
objectively locate the material boundaries of coherent vortices in
two-dimensional Navier--Stokes turbulence. We show that these boundaries are
optimal in the sense that any closed curve in their exterior will lose
coherence under material advection. Through a detailed comparison, we find that
other available Eulerian and Lagrangian techniques significantly underestimate
the size of each coherent vortex.
