Chaotic Advections in a Time-Dependent, Three-Dimensional, Ekman-Driven Eddy

Our work focuses on the existence and arrangement of isolate regions of Lagrangian chaos in models of time-dependent, 3D flows with horizontal swirl and vertical overturning. Possible applications include mesoscale and sub-mesoscale ocean eddies, hurricanes, and convection cells, and the results demonstrate that chaotic stirring in such features can be highly nonhomogeneous. As a simple model we consider the flow in a rotating cylinder, driven by a time-dependent stress at the surface. Using numerical solutions and a multiple-scale analytical approach, we locate regions of Lagrangian chaos and compute the material barriers that contain them. These barriers are usually topological tori that evolve in time and can be quite exotic. If all the forcing is strong enough, all of these barriers can be destroyed, the entire flow becomes chaotic, and tracers are rapidly mixed throughout. We speculate on a way in which the stirring and mixing might be parameterized using ideas from critical layer theory.