Hydrodynamic interactions and extreme particle clustering in turbulence

Expanding recent observations by Hammond & Meng (J. Fluid Mech., vol. 921, 2021, A16), we present a range of detailed experimental data of the radial distribution function (r.d.f.) of inertial particles in isotropic turbulence for different Stokes number, St, showing that the r.d.f. grows explosively with decreasing separation r, exhibiting r(-6) scaling as the collision radius is approached, regardless of St or particle radius a. To understand such explosive clustering, we correct a number of errors in the theory by Yavuz et al. (Phys. Rev. Lett., vol. 120, 2018, 244504) based on hydrodynamic interactions between pairs of small, weakly inertial particles. A comparison between the corrected theory and the experiment shows that the theory by Yavuz et al. underpredicts the r.d.f. by orders of magnitude. To explain this discrepancy, we explore several alternative mechanisms for this discrepancy that were not included in the theory and show that none of them are likely the explanation. This suggests new, yet-to-be-identified physical mechanisms are at play, requiring further investigation and new theories.

Automated summary

Expanding on recent observations, this study provides detailed experimental data on the radial distribution function (rdf) of inertial particles in isotropic turbulence for different Stokes numbers (St). The results indicate explosive growth of rdf with decreasing separation, showing a r(-6) scaling near the collision radius regardless of St or particle radius. By correcting errors in previous theories and comparing with experiments, this study reveals significant underestimation of rdf by previous theory and explores alternative mechanisms that fail to explain the discrepancy. This suggests the presence of new, unidentified physical mechanisms that require further investigation and new theories.