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 (2D) vector fields. The flows analyzed here are numerical solutions to the barotropic, beta-plane, potential vorticity equation with viscosity, where the partial differential equation (PDE) parameters have been chosen so that the solution evolves to a meandering jet. Numerical methods for approximating invariant manifolds of hyperbolic fixed points for maps are successfully applied to the aperiodic vector field where regions 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 intersections identified with chaotic transport in 2D maps, with the lobe geometry approximately recurring on a time scale equal to the dominant time period in the vector field. The resulting lobe structures provide time-dependent estimates for the transport between different flow regimes. Additional numerical experiments show that the computation of such lobe geometries are very robust relative to variations in interpolation, integration and differentiation schemes.