  Statistical properties of circulation encode relevant information about the
multi-scale structure of turbulent cascades. Recent massive computational
efforts have posed challenging theoretical issues, as the dependence of
circulation moments upon Reynolds numbers and length scales, and the specific
shape of the heavy-tailed circulation probability distribution functions. We
address these focal points in an investigation of circulation statistics for
planar cuts of three-dimensional flows. The model introduced here borrows ideas
from the structural approach to turbulence, whereby turbulent flows are
depicted as dilute vortex gases, combined with the standard Obukhov-Kolmogorov
phenomenological framework of small-scale intermittency. We are able to
reproduce, in this way, key statistical features of circulation, in close
agreement with empirical observations compiled from direct numerical
simulations.
