Probability Distribution of Velocity Circulation in Three-Dimensional Turbulence

Abstract

The probability distribution functions (PDFs) of the circulation of velocity in three-dimensional decaying isotropic turbulence are examined using the database of numerical simulation based on the spectral method. It is shown that the standard deviation increases nearly as A^2⁄3 where A is the area of the loop. The PDFs change from exponential to Gaussian as the size increases. The former agrees well with the prediction by Migdal (1993, hep-th/9303130), although the latter deviates from it. A modification is proposed to explain the Gaussian distribution with the A^2⁄3 dependence.