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 vector elds. The ows analyzed here are numerical solutions to the barotropic, -plane, potential vorticity equation with viscosity, where the pde parameters have been chosen so that the solution evolves to a meandering jet. Numerical methods for approximating invariant manifolds of hyperbolic xed points for maps are successfully applied to the aperiodic vector eld where regions of strong hyperbolicity persist for long times relative to the dominant time period in the ow. Cross sections of these two-dimensional \stable" and \unstable" manifolds show the characteristic transverse intersections identi ed with chaotic transport in 2-D maps, with the lobe geometry approximately recurring on a time scale equal to the dominant time period in the vector eld. The resulting lobe structures provide time-dependent estimates for the transport between di erent ow regimes. Additional numerical experiments show that the computation of such lobe geometries are very robust relative to variations in interpolation, integration and di erentiation schemes.