Dynamics, Statistics and Vortex Crystals in the Relaxation of 2D Turbulence

Abstract

Magnetically confined electron columns evolve in (r, ) as essentially inviscid, incompressible 2D fluids with a single sign of vorticity. Turbulent initial states with 50–100 vortices relax due to vortex merger and filamentation, in general agreement with a recent dynamical scaling theory. However, this relaxation sometimes halts when 3–20 vortices “anneal” into a fixed pattern, or “vortex crystal.” A new “regional 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. However, simulations show that the character of the relaxed state generally depends strongly on initial conditions and dynamics.