QUANTIFYING TRANSPORT IN NUMERICALLY GENERATED VELOCITY-FIELDS

Geometric methods from dynamical systems are used to study Lagrangian transport in numerically generated, time-dependent, two-dimensional (2 D) vector fields. The flows analyzed here are numerical solutions to t he barotropic, beta-plane, potential vorticity equation with viscosity , where the partial differential equation (PDE) parameters have been c hosen so that the solution evolves to a meandering jet. Numerical meth ods for approximating invariant manifolds of hyperbolic fixed points f or maps are successfully applied to the aperiodic vector field where r egions of strong hyperbolicity persist for long times relative to the dominant time period in the flow. Cross sections of these 2D ''stable' ' and ''unstable'' manifolds show the characteristic transverse inters ections identified with chaotic transport in 2D maps, with the lobe ge ometry approximately recurring on a time scale equal to the dominant t ime period in the vector field. The resulting lobe structures provide time-dependent estimates for the transport between different flow regi mes. Additional numerical experiments show that the computation of suc h lobe geometries are very robust relative to variations in interpolat ion, integration and differentiation schemes.