  Methods of dynamical system's theory are used for numerical study of
transport and mixing of passive particles (water masses, temperature, salinity,
pollutants, etc.) in simple kinematic ocean models composed with the main
Eulerian coherent structures in a randomly fluctuating ocean -- a jet-like
current and an eddy. Advection of passive tracers in a periodically-driven flow
consisting of a background stream and an eddy (the model inspired by the
phenomenon of topographic eddies over mountains in the ocean and atmosphere) is
analyzed as an example of chaotic particle's scattering and transport. A
numerical analysis reveals a nonattracting chaotic invariant set $\Lambda$ that
determines scattering and trapping of particles from the incoming flow. It is
shown that both the trapping time for particles in the mixing region and the
number of times their trajectories wind around the vortex have hierarchical
fractal structure as functions of the initial particle's coordinates.
Scattering functions are singular on a Cantor set of initial conditions, and
this property should manifest itself by strong fluctuations of quantities
measured in experiments. The Lagrangian structures in our numerical experiments
are shown to be similar to those found in a recent laboratory dye experiment at
Woods Hole. Transport and mixing of passive particles is studied in the
kinematic model inspired by the interaction of a jet current (like the Gulf
Stream or the Kuroshio) with an eddy in a noisy environment. We demonstrate a
non-trivial phenomenon of noise-induced clustering of passive particles and
propose a method to find such clusters in numerical experiments. These clusters
are patches of advected particles which can move together in a random velocity
field for comparatively long time.
