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Title: Rate of sling events and caustics for inertial particles
Plain: 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: 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.
Settled by: 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.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status note: 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.
Posed since: 2006