Intricate relations among particle collision, relative motion and clustering in turbulent clouds: computational observation and theory

Considering turbulent clouds containing small inertial particles, we investigate the effect of particle collision, in particular collision-coagulation, on clustering and relative motion. We perform direct numerical simulation (DNS) coagulating particles isotropic flow regime Stokes number ($St=0.001-0.54$) find that, due to radial distribution functions (RDFs) fall-off dramatically at scales $r \sim d\,\,$ (where $d$ is diameter) but finite values, while mean radial-component velocities (MRV) increase sharply magnitudes. Based a previously proposed Fokker-Planck (drift-diffusion) framework, derive theoretical account relationship among collision-coagulation rate, RDF MRV. The theory includes contributions from turbulent-fluctuations absent earlier mean-field theories. show numerically that accurately accounts for DNS results (i.e., given an accurate RDF, could produce MRV). Separately, also propose phenomenological model directly predict MRV it when calibrated using fourth moments fluid velocities. use general solution RDF. uncover paradox: past empirical success differential version theoretically unjustified. see further shape-preserving reduction (and MRV) gravitational settling parameter ($S_g$) order $O(1)$. Our demonstrate strong coupling between imply isolated studies either or have limited relevance predicting collision rate.