Sandpiles as a Paradigm for Turbulent Transport

In order to understand the complex dynamics of turbulent (anomalous) transport in magnetic confinement devices a simple Self Organized Criticality (SOC) model based on the dynamics of avalanches down a running sandpile has been used. The cellular automata rules governing the system are simply: if the local gradient (Zn) is greater than a critical gradient the sandpile become locally unstable and a given number (Nf) of grains fall down to the next site down. This simple model displays remarkably rich dynamics which have many characteristics in common with the observed transport dynamics in magnetic confinement devices. Therefore this type of model is used to explore the interaction between this avalanche like transport and the sheared flows which are so important in plasma confinement. From this model useful insight has been gained into the transport dynamics and the two apparent transport regimes in plasma confinement devices




In the animations below, you will be looking at the face of the sandpile (like the face of the sandpile on the left). The light colored squares, in the animation, are unstable (avalanching) sites while the dark colored squares (the rest) are stable sites. The system is periodic across the pile, closed at the top and open at the bottom. You will be able to see avalanches of all sizes (a characteristic feature of SOC systems) as well as unstable sites propagating up the pile (again something characteristic of SOC systems).



Animation of a running sandpile with and without sheared flow


No Shear in the system Shear in middle 3rd of system

unsheared gif moviesheared gif movie

Note how the transport events (the avalanches) span all sizes in the unsheared system. This leads to very efficient transport (a bad thing if you are trying to confine a plasma). However in the sheared region the large transport events are torn apart which reduces the effective transport and therefore improves the confinement.


A simulation of a turbulent system used to validate the SOC model


This 3-D nonlinear computation is of Resistive G-mode turbulence driven by the pressure gradient. The figure on the left shows the density in which the long, transport event, scalelengths are visible. The figure on the right shows the potential in which the smaller, fluctuation, scalelengths are apparent. This agrees with the simple SOC model.


For more information see

The Dynamics of Marginality and Self-organized Criticality as a Paradigm for Turbulent Transport, D. E. Newman, B. A. Carreras, P. H. Diamond and T. S. Hahm, Phys. Plasmas 3 (5) May 1996.

The Dynamics of Sand piles with sheared flow, D. E. Newman, B. A. Carreras and P. H. Diamond Phys. Letters A 218 July (1996).

A Model Realization of Self-Organized Criticality for Plasma Confinment, B. A. Carreras, D. E. Newman, V. E. Lynch, and P. H. Diamond, Phys. Plasmas 3 (8) August 1996.



Last changed on 11 Nov 1998

This page is maintained by David Newman