Abstract
We present results on the connection between the vorticity equation and the shape and evolution of the single-point vorticity probability density function. The statistical framework for these observations is based on the classical hierarchy of evolution equations for the probability density functions by Lundgren, Novikov, and Monin combined with conditional averaging of the unclosed terms. The numerical evaluation of these conditional averages provides insights into the intimate relation of dynamical effects such as vortex stretching and vorticity diffusion and non-Gaussian vorticity statistics.
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