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

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.

References in corpus (3)

• Non-diffusive transport in plasma turbulence: a fractional diffusion approach
• Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
• Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow

Cited by in corpus (5)

• Short note on the emergence of fractional kinetics
• Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Levy Stable Processes
• Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations
• Phase transitions in the fractional three-dimensional Navier-Stokes equations
• Global scaling of the heat transport in fusion plasmas