On the Probability Distribution of Velocity Circulation in Three-Dimensional Turbulence

TL;DR

This paper investigates the probability distribution of velocity circulation in 3D turbulence, showing how it varies with loop size and proposing a modification to explain observed Gaussian distributions.

Contribution

It provides new insights into the distribution of velocity circulation in 3D turbulence and proposes a modification to existing models to account for Gaussian behavior.

Findings

Standard deviation scales as A^{2/3}

PDFs transition from exponential to Gaussian with increasing size

Proposed modification explains Gaussian distribution with A^{2/3} dependence

Abstract

The probability distribution functions of the circulation of velocity in three-dimensional decaying isotropic turbulence are examined by the database of the numerical simulation based on the pseudospectral 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 becomes large. The former agrees well with the prediction by Migdal (1993), although the latter does not match. A modification is proposed to explain the gaussian distribution with the $A^{2/3}$ dependence.