Vortex properties of two-dimensional turbulence

Abstract

Novel physical‐space vortex properties of nearly inviscid, unforced two‐dimensional (2‐D) turbulence are presented. They are obtained from the analysis of a large ensemble of calculations all beginning with a random distribution of vortex patches of equal vorticity magnitude on a spherical surface. The numerical method (MACS) is a combination of contour dynamics/surgery (CD/CS) and a moment expansion for calculating separated vortex interactions. This method calculates approximately 100 times faster than CD/CS thereby permitting the formation of a large database for obtaining meaningful statistics. The numerical method can resolve a much wider range of spatial scales than conventional (pseudospectral) methods, and it is found that the statistical vortex properties produced differ in significant respects from those obtained previously. This conclusion is drawn from not just one set of calculations, but three at different spatial resolutions. While algebraic decay of basic flow statistics (e.g., enstrophy, vortex population) is observed at late times, the decay exponents are smaller than previously obtained and furthermore do not come in the ratios suggested by the recently proposed ‘‘universal scaling theory.’’ In addition, the vortex number density distribution is not found to be self‐similar but steepens continuously and appreciably with decreasing vortex size. This forces a reevaluation of the nature of 2‐D turbulence in the inviscid limit. A proper description of this limit needs (more) quantitative information concerning the most probable vortex interactions. Such interactions will not be between just two vortices, as is commonly supposed.