Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows

Lagrangian coherent structures (LCSs) are exceptional material surfaces that act as cores of observed tracer patterns in fluid flows (see [1,2] for reviews). For oceanic flows, the tracers of interest include salinity, temperature, contaminants, nutrients and plankton—quantities that play an important role in the ecosystem and even in the climate. Fluxes of these quantities are typically dominated by advective transport over diffusion. An important component of advective transport in the ocean is governed by mesoscale eddies, i.e. vortices of 100–200 km in diameter. While eddies also stir and mix surrounding water masses by their swirling motion, here we focus on eddies that trap and carry fluid in a coherent manner. Eddies of this kind include the Agulhas rings of the Southern Ocean. They are known to transport massive quantities of warm and salty water from the Indian Ocean into the Atlantic Ocean [3]. Current limitations on computational power prevent climate models from resolving mesoscale eddies in their flow field. As the effect of mesoscale eddies on the global circulation is significant [4], the correct parametrization of eddy transport is crucial for the reliability of these models. As a consequence, there is