Hydrodynamic interactions and extreme particle clustering in turbulence

From new detailed experimental data, we found that the Radial Distribution Function (RDF) of inertial particles in turbulence grows explosively with $r^{-6}$ scaling as the collision radius is approached. We corrected a theory by Yavuz et al. (Phys. Rev. Lett. 120, 244504 (2018)) based on hydrodynamic interactions between pairs of weakly inertial particles, and demonstrate that even this corrected theory cannot explain the observed RDF behavior. We explore several alternative mechanisms for the discrepancy that were not included in the theory and show that none of them are likely the explanation, suggesting new, yet to be identified physical mechanisms are at play.