A mathematical investigation of stirring and mixing of passive tracers by an anisotropic flow field characterized by chaotic advection

Stirring and mixing plays a central role in the oceans and atmosphere, where the large-scale circulation is characterized by strong anisotropy. When the tracer evolution has no effect on the inertia of the velocity field, i.e., the tracer is passive, the governing evolution equation for the tracer is linear no matter how complicated the advecting velocity field is. Exploiting the linearity of the problem, we present a general approach for computing analytical solutions to the governing tracer equation for prescribed, time-evolving velocity fields. We apply it to analyze the evolution of a passive tracer in the case the advecting velocity field is a form of renewing flow, a prototype of chaotic advection, with stronger transport along a preferred axis. We consider both the freely decaying case and the case with a source of scalar variance (equilibrated), and discuss the possibility to generalize this approach for reacting tracers (biogeochemistry) and more complicated time-varying velocity fields.