New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles

In this paper, we contrast two theoretical models for the spatial clustering of inertial particles in isotropic turbulence, one by Chun et al (2005 J. Fluid Mech. 536 219) and the other by Zaichik et al (2007 Phys. Fluids 19 113308). Although their predictions for the radial distribution function are similar in the regime St << 1, they appear to describe the physical mechanism responsible for the clustering in quite different ways. We demonstrate why the theories generate such similar results in the regime St << 1 by showing that the clustering mechanism in the Chun et al theory captures the leading order effects of the clustering mechanism in the Zaichik et al theory for St << 1. However, outside of this regime, the similarity between the predictions of the theories breaks down, and we consider the sources of the differences as well as the physical meaning and implications of the differences. Using DNS data we then show that the clustering mechanism described by the Zaichik et al theory accurately describes the clustering up to St approximate to 1, and we identify a possible source of error for some of the slight quantitative discrepancies at larger St. We then compare these theories with others in the literature and attempt to reconcile as many of the physical explanations for clustering as we can. Finally, we consider the relationship between clustering in isotropic turbulence and the near-wall accumulation of inertial particles in a turbulent boundary layer, and how they scale with the Stokes number in the weak inertia limit.