Stirring: The Eckart paradigm revisited

This report provides a topical review of transport in geophysical scale fluids. Rather than presenting an extensive synopsis of the literature, we attempt to connect some recent developments with an incisive 1948 paper by Eckart [1] in which three phases in the evolution of a tracer in turbulent flows were outlined and discussed. The interest here is on the intermediate or stirring phase, which is dominated by the fluid deformation rate. We relate Eckart’s concept of stirring with recent efforts to identify ephemeral spatio-temporal channels that provide a template for transport in geophysical fluid flows. Heretofore such studies have been restricted to a few selected surfaces in the ocean or atmosphere. An application to a large ocean eddy in the Gulf of Mexico illustrates the methodology and shows that the eddy exchanges mass with its environment through material channels identified in the Lagrangian frame by finite-time dynamical systems techniques. We extend previous studies by determining the vertical extent of these transport pathways. The key finding is that the time-dependent geometric structures, which lead to formation of these pathways, retain their coherence well into the water column. Finally, we comment on the significance of these findings on parameterizations of transport processes in predictive models and on the life cycle of ocean mesoscale eddies.