Forecasting long-lived Lagrangian vortices from their objective Eulerian footprints

Abstract

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- 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.