Universal decay of vortex density in two dimensions

Abstract

Recent numerical and experimental results for freely decaying two-dimensional turbulence point to a universal decay in vortex density, ϱ∼t-ξ (ξ ⋍ 0.73), from highly turbulent to laminar, vortex-free flows. This vortex decay has been successfully described in terms of a point-vortex dynamics, in close resemblance to the vortex dynamics for the two-dimensional Ginzburg-Landau equation. Here, we add numerical evidence and give theoretical arguments that the vortex density at late times follows the conjectured power law with ξ = 34.