Characteristics of Two-Dimensional Turbulence That Self-Organizes into Vortex Crystals

Experiments have found that freely relaxing turbulence in inviscid, incompressible two-dimensional Euler flows can self-organize into ordered structures—vortex crystals—in which a number $N_c\sim 2–20$ of strong vortices form stable, rigidly rotating patterns in a low vorticity background. In this paper we show that $N_c$ can be roughly predicted from properties of the flows in the early stage of the turbulent relaxation.