Properties of velocity circulation in three-dimensional turbulence

Properties of velocity circulation in three-dimensional turbulence are studied using data from high-resolution direct numerical simulation of Navier-Stokes equations. The probability density function (PDF) of the circulation depends on the area of the closed contour for which circulation is calculated, but not on the shape of the contour. For contours lying within the inertial range, the PDF has a Gaussian core with conspicuous exponential tails, indicating that intermittency plays an important role in circulation statistics. The measured scaling exponents are anomalous and substantially smaller than those implied by Kolmogorov's phenomenology. © 1996 American Physical Society.