Geometric methods from dynamical systems are used to characterize Lagrangian transport in numerically-generated, time-dependent, two-dimensional velocity fields. In many geophysical models the velocity field is given only as a numerical solution to an appropriate governing system of partial differential equations. This talk presents current progress in developing numerical techniques for characterizing chaotic-like transport in such numerical vector fields, where the vector field has aperiodic time-dependence and is known only on a finite time interval. Invariant manifolds are constructed numerically to create a template for describing the exchange of fluid between different flow regimes. Results are presented from simulations modeling geophysical flows.