Statistical laws of velocity circulation in homogeneous turbulence

Statistical properties of the velocity circulation in turbulence are studied using data from direct numerical simulation (DNS) of Navier-Stokes equations. The probability density function (PDF) of circulation depends on the area of the closed contour along which the circulation is calculated. The vorticity field obtained in DNS is decomposed into the strong component and the weak component. It is found that the circulation associated with the weak component is approximately self-similar with respect to the area a. The circulation associated with the strong component is modeled appropriately by a compound Poisson statistics of vortex filaments in the asympotic limit of the large area a.