Investigating the small-scale structure of clouds using the δ-correlated closure: effect of particle inertia, condensation/evaporation and intermittency

Abstract

Equations for the first and second moments of particle density are closed exactly in the large Prandtl number limit, using the δ-correlated closure whereby the turbulent velocity field is assumed to rapidly decorrelate in time. Results are summarized from two recent studies that have investigated the effect of both particle inertia and condensation/evaporation on the viscous–convective subrange. Analytic expressions for the spectrum of inertial particles are presented which show that clumping (preferential concentration) does not occur for Stokes number ( St) less than about 0.2. Also presented are analytic expressions for the scalar spectrum of cloud liquid water density derived from a simple mean-field model of condensation/evaporation. The model reproduces new experimental observations [J. Geophys. Res. 104 (1999) 6123] of cloud liquid water content (LWC) fluctuations that exhibit anomalous near-inertial scaling. For the first time, the effect of high Reynolds number ( Re λ) velocity field intermittency on preferential concentration is considered in a quantitative manner. A Re λ-dependent effective Stokes number ( St eff) is derived that is proportional to the square root of the flatness factor of the longitudinal velocity derivative. In the atmospheric boundary-layer, St eff≈2.7 St. These results support Shaw et al.'s [J. Atmos. Sci. 55 (1998) 1965] hypothesis that velocity field intermittency tends to increase preferential concentration at St<1. However, in contrast with Shaw et al., I demonstrate that, in real turbulence, vortex tubes do not statistically affect St eff and, hence, preferential concentration.