People

Research

Publications

Links

 

 

 Understanding particle transport is a problem of theoretical and practical importance in plasma physics, geophysical fluid dynamics, laboratory experiments and engineering. Because of the intrinsic unpredictability that particle trajectories typically exhibit, one has to abandon the idea of studying individual trajectories, and consider instead an statistical approach in which transport is characterized by ensemble averaged properties of particle motion. A commonly used statistical measures of transport is the variance, is the particle displacement, and < > denotes average over an ensemble of particles. One of the most basic transport problems is the study of the long-time behavior of the variance and of the probability density function (PDF) of particle displacement, A naive approach of this problem would assume that, at long timesis a Gaussian distribution evolving in time according to an advection-diffusion equation with a mean transport velocity, and an effective diffusivity, .Although this approach has been fruitful in the study of passive scalar transport in homogeneous isotropic turbulence, and in the study of Brownian motion, it fails when there is anomalous diffusion.Anomalous diffusion occurs when there is not a well-defined diffusion coefficient, i.e. when in which case D is either zero or infinite. Our general goal is to study anomalous diffusion due to coherent structures (e.g. zonal flows and vortices) in systems of interest to plasma physics and geophysical fluid dynamics.