Relaxation of 2D turbulence of vortex crystals

Abstract

A magnetically confined electron column evolves in ( r, θ) as an essentially inviscid, incompressible 2D fluid with a single sign of vorticity. Turbulent initial states with 50–100 vortices relax due to vortex merger and filamentation, in general agreement with recent scaling theories. However, this relaxation is sometimes halted when 3–20 vortices “anneal” into a fixed pattern, or “vortex crystal”. 2D vortex-indashcell simulations reproduce this effect, demonstrating that the vortex “cooling” is independent of fine-scale viscosity, but strongly dependent on the strength of the weak background vorticity. A new “restricted maximum fluid entropy” theory predicts the crystal patterns and background vorticity distribution, by assuming conservation of the robust flow invariants and preservation of the intense vortices.