The Geometry and Statistics of Mixingin Aperiodic

The relationship between the statistical and geometric properties of particle motion in aperiodic, two-dimensional ows is examined. Finite-time invariant manifolds associated with transient hyperbolic trajectories are shown to divide the ow into distinct regions with similar statistical behavior. In particular, numerical simulations of simple, eddy resolving barotropic ows indicate that there exists a close correlation between such geometric structures and patchiness plots which describe the distribution of Lagrangian average velocity over initial conditions. For barotropic turbulence, a similar relationship is identiied at intermediate time scales where anomalous dispersion rates are found.