Intricate Relations Among Particle Collision, Relative Motion and Clustering in Turbulent Clouds: Computational Observation and Theory

TL;DR

This study combines direct numerical simulations and theoretical models to analyze how particle collision and coagulation influence clustering and relative velocities in turbulent clouds, revealing strong coupling effects and limitations of previous isolated approaches.

Contribution

It introduces a comprehensive theory linking collision rate, RDF, and MRV, incorporating turbulent fluctuations, and validates it against DNS results, advancing understanding of particle dynamics in turbulence.

Findings

Collision-coagulation causes RDF to sharply decrease at particle scale.

Theoretical model accurately predicts MRV from RDF data.

Shape-preserving RDF and MRV reduction occurs with gravitational settling parameter.

Abstract

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