  We derive a non-dimensional metric to quantify the expected Lagrangian
persistence of objectively defined Eulerian vortices in two-dimensional
unsteady flows. This persistence metric is the averaged deviation of the
vorticity from its spatial mean over the Eulerian vortex, normalized by the
instantaneous material leakage from the Eulerian vortex. The metric offers a
model-independent and frame-independent tool for uncovering the instantaneous
Eulerian signature of long-lived Lagrangian vortices. Using satellite-derived
ocean velocity data, we show that Lagrangian vortex-persistence predictions by
our metric significantly outperform those inferred from other customary
Eulerian diagnostics, such as the potential vorticity gradient and the
Okubo-Weiss criterion.
