Abstract. We study the relation between changes in the Eulerian topology of a two dimensional flow and the mixing of fluid particles between qualitatively different regions of the flow. In general time dependent flows, streamlines and particle paths are unrelated. However, for many mesoscale oceanographic features such as detaching rings and meandering jets, the rate at which the Euierian structures evolve is considerably slower than typical advection speeds of Lagrangian tracers. In this note we show that for two-dimensional, adiabatic fluid flows there is a direct relationship between observable changes in the topology of the Eulerian field and the rate of transport of fluid particles. We show that a certain class of flows is amenable to adiabatic or near adiabatic analysis, and, as an example, we use our results to study the chaotic mixing in the Dutkiewicz and Paldor (1994) kinematic model of the interaction of a meandering barotropic jet with a strong eddy.