How long do particles spend in vortical regions in turbulent flows?

We consider passive, heavy, inertial, particles (HIP) in three-dimensional, homogeneous, and isotropic turbulence. Whether a particle is in a vortical regions or not is determined by the two invariants of the (flow) velocity gradient matrix , $Q$ and $R$, at the position of the parti cle. Using direct numerical simulations, we calculate the probability distribution functions (PDFs) of the first-passage-time of a tracer or a HIP in a vortical region. The corresponding PDF in two dimensions is known to show power-law tail. In three dimensions we find that the PDF possesses exponential tail with a characteristic time of the order of large-eddy-turnover-time of the flow.