Non-diffusive, non-local transport in fluids and plasmas

• Main Author: D. del-Castillo-Negrete
• Format: Article
• Language: English
• Published: Copernicus Publications 2010-12-01
• Series: Nonlinear Processes in Geophysics
• Online Access: http://www.nonlin-processes-geophys.net/17/795/2010/npg-17-795-2010.pdf

A review of non-diffusive transport in fluids and plasmas is presented. In the fluid context, non-diffusive chaotic transport by Rossby waves in zonal flows is studied following a Lagrangian approach. In the plasma physics context the problem of interest is test particle transport in pressure-gradient-driven plasma turbulence. In both systems the probability density function (PDF) of particle displacements is strongly non-Gaussian and the statistical moments exhibit super-diffusive anomalous scaling. Fractional diffusion models are proposed and tested in the quantitative description of the non-diffusive Lagrangian statistics of the fluid and plasma problems. Also, fractional diffusion operators are used to construct non-local transport models exhibiting up-hill transport, multivalued flux-gradient relations, fast pulse propagation phenomena, and "tunneling" of perturbations across transport barriers.