  Dynamical systems theory approach has been successfully used in physical
oceanography for the last two decades to study mixing and transport of water
masses in the ocean. The basic theoretical ideas have been borrowed from the
phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian
chaos in mechanics. The starting point for analysis is a velocity field
obtained by this or that way. Being motivated by successful applications of
that approach to simplified analytic models of geophysical fluid flows,
researchers now work with satellite-derived velocity fields and outputs of
sophisticated numerical models of ocean circulation. This review article gives
an introduction to some of the basic concepts and methods used to study chaotic
mixing and transport in the ocean and a brief overview of recent results with
some practical applications of Lagrangian tools to monitor spreading of
Fukushima-derived radionuclides in the ocean.
