Rate of sling events and caustics for inertial particles
In plain words
Heavy particles in turbulence are sometimes flung out of intense whirls so that particles at the same place move with very different speeds, which raises collision rates. The frequency of these events at small particle inertia is predicted but not measured accurately.
Precise statement
Heavy particles with Stokes number $\mathrm{St} = \tau_p/\tau_\eta$ (particle response time over Kolmogorov time) form caustics where their velocity field becomes multivalued. Theory predicts a caustic formation rate $\sim \operatorname{exp}(-A/\mathrm{St})$ at small St (Wilkinson, Mehlig, Bezuglyy 2006). Determine $A$, the prefactor and their $\mathrm{Re}_\lambda$ dependence in 3D Navier-Stokes turbulence.
What would settle it
DNS over a decade in $\mathrm{Re}_{\lambda}$ and laboratory particle tracking measuring caustic rates at St from 0.05 to 0.5, fitted to the predicted form.
Status in the literature
A theory based on velocity-gradient statistics predicts sling-event rates and their growth with $\mathrm{Re}_\lambda$, validated by DNS at moderate $\mathrm{Re}_\lambda$ (Batge, Fouxon, Wilczek, arXiv:2208.05384); tests at cloud-like $\mathrm{Re}_\lambda$ are lacking.