  We model Lagrangian lateral mixing and transport of passive scalars in
meandering oceanic jet currents by two-dimensional advection equations with a
kinematic stream function with a time-dependent amplitude of a meander imposed.
The advection in such a model is known to be chaotic in a wide range of the
meander's characteristics. We study chaotic transport in a stochastic layer and
show that it is anomalous. The geometry of mixing is examined and shown to be
fractal-like. The scattering characteristics (trapping time of advected
particles and the number of their rotations around elliptical points) are found
to have a hierarchical fractal structure as functions of initial particle's
positions. A correspondence between the evolution of material lines in the flow
and elements of the fractal is established.

Chaotic Dynamics;Atmospheric and Oceanic Physics