Material spreading and mixing by oceanic mesoscale eddies are analyzed in an 
idealized, numerical model of the wind-driven, mid-latitude ocean circulation. 
The analyses are based on ensembles of Lagrangian particle trajectories. The 
single-particle dispersion, which describes the spreading, is generally 
anisotropic and inhomogeneous, and in most places it is not diffusive (i.e., not 
linear in time) during intermediate-time intervals after release. A hierarchy of 
inhomogeneous and non-stationary stochastic models of material transport is 
rigorously formulated, its properties are described, and each model is fitted to 
an eddy-resolving solution of idealized, mid-latitude ocean gyres. The models 
provide more skillful parameterizations of the sub-grid-scale material transport 
induced by unresolved mesoscale eddies than the commonly used eddy-diffusion 
model.