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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 17, issue 6
Nonlin. Processes Geophys., 17, 795–807, 2010
https://doi.org/10.5194/npg-17-795-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Nonlinear plasma waves in space and laboratories

Nonlin. Processes Geophys., 17, 795–807, 2010
https://doi.org/10.5194/npg-17-795-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

Review article 20 Dec 2010

Review article | 20 Dec 2010

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

D. del-Castillo-Negrete D. del-Castillo-Negrete
  • Oak Ridge National Laboratory, Oak Ridge, TN, USA

Abstract. 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.

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