TURBULENCE IN 2-DIMENSIONAL PLASMAS AND FLUIDS

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 t o 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 th e spontaneous appearance of macroscopic clumps of charge or vorticity and may represent a stage of 2D turbulence. However, this raises the b asic question; can a limited number of particles ever represent the be haviour of a continuous fluid? At first sight the two models are incom patible. The particles are conservative, have finite degrees of freedo m and few isolating invariants. The fluid has infinite degrees of free dom 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-parti cles are chosen appropriately. Roughly speaking, a small viscosity des troys invariants of an ideal fluid and limits its degrees of freedom, while preserving its essentially conservative behaviour.