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

TL;DR

This paper reviews non-diffusive transport phenomena in fluids and plasmas, highlighting non-Gaussian statistics, super-diffusive behavior, and the application of fractional diffusion models to describe complex transport processes.

Contribution

It introduces fractional diffusion models to quantitatively describe non-diffusive, non-local transport in fluids and plasmas, including phenomena like up-hill transport and tunneling across barriers.

Findings

Particle displacement PDFs are strongly non-Gaussian.

Transport exhibits super-diffusive anomalous scaling.

Fractional diffusion models effectively describe non-local transport phenomena.

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.