Tracer dynamics in a flow of driven vortices

Abstract

From numerical computations of the two-dimensional Navier-Stokes equations, we derive a low-dimensional stream-function model that captures the essential properties of the dynamics of an array of driven vortices in time-periodic regime. Using this analytical model, we study the Lagrangian dynamics of passive tracers and show that it is essentially controlled by the existence of a chaotic saddle. We obtain its stable and unstable manifolds, which in turn, yield an approximation of the chaotic saddle in terms of their intersections. By introducing symbolic dynamics, the spatiotemporal properties of the flow, including an alternative approximation of the chaotic saddle, are described in terms of measures of complexity.