Turbulence in two-dimensional plasmas and fluids

Abstract

In two dimensions (2D), a guiding-centre plasma and an inviscid fluid can be described by a continuum model or by quasi-particles (filaments) with Coulomb interaction. Other 2D continuum models are equivalent to quasi-particles with a screened Coulomb interaction. Such 2D systems of quasi-particles have negative temperature equilibria, characterized by large fluctuations. In the continuum models this corresponds to the spontaneous appearance of macroscopic clumps of charge or vorticity and may represent a stage of 2D turbulence. However, this raises the basic question; can a limited number of particles ever represent the behaviour of a continuous fluid? At first sight the two models are incompatible. The particles are conservative, have finite degrees of freedom and few isolating invariants. The fluid has infinite degrees of freedom and is conservative only if dissipation is ignored - when it has an infinity of invariants. Despite these fundamental differences, the two systems may be reconciled if the fluid is viscous and the quasi-particles are chosen appropriately. Roughly speaking, a small viscosity destroys invariants of an ideal fluid and limits its degrees of freedom, while preserving its essentially conservative behaviour.