How turbulence enhances coalescence of settling particles with applications to rain in clouds

Abstract

From theoretical, numerical and experimental studies of small inertial particles with density equal to β (>1) times that of the fluid, it is shown that such particles are ‘centrifuged’ out of vortices and eddies in turbulence. Thus, in the presence of gravitational acceleration g , their average sedimentation velocity V T in a size range just below a critical radius a cr is increased significantly by up to about 80%. We show that in fully developed turbulence, a cr is determined by the circulation Γ k of the smallest Kolmogorov micro-scale eddies, but is approximately independent of the rate of turbulent energy dissipation ϵ , because Γ k is about equal to the kinematic viscosity ν . It is shown that a cr varies approximately like and is about 20 μm (±2 μm) for water droplets in most types of cloud. New calculations are presented to show how this phenomena causes higher collision rates between these ‘large’ droplets and those that are smaller than a cr , leading to rapid growth rates of droplets above this critical radius. Calculations of the resulting droplet size spectra in cloud turbulence are in good agreement with experimental data. The analysis, which explains why cloud droplets can grow rapidly from 20 to 80 μm irrespective of the level of cloud turbulence is also applicable where a cr ∼1 mm for typical sand/mud particles. This mechanism, associated with unequal droplet/particle sizes is not dependant on higher particle concentration around vortices and the results differ quantitatively and physically from theories based on this hypothesis.

Violent expiratory events: on coughing and sneezing

“…Note that the addition of beads modifies the dynamics of the cloud, decreasing the entrainment coefficient and so increasing the particle range. Quite generally, turbulence affects the mixing and coalescence of suspended particles and droplets in various multiphase flows (Ghosh et al 2005). The best fit entrainment coefficient for the multiphase cloud was lower than for homogeneous clouds as is consistent with the recent observations of Lai et al (2013).…”

The role of air turbulence in warm rain initiation

“…In this case, the first condition, Equation (2), must also be satisfied to obtain a significant η G value. Other conditions for enhanced geometric collision through particle clustering would be τ p ∼ τ k (Wang and Maxey, 1993) and F p = τ p 3 |g| 2 /ν ∼ 1 (Ghosh et al, 2005;Ayala et al, 2008b). For ν=0.17 cm 2 /s, |g|=980 cm/s 2 , ρ w /ρ ≈1000, the condition F p ∼ 1 implies a droplet radius at about 21 µm, independent of the flow dissipation rate.…”

“…The analysis in Falkovich et al (2002) implies that preferential concentration of droplets and local fluid acceleration due to cloud turbulence can substantially accelerate the formation of large droplets that trigger rain. Another analysis (Ghosh et al, 2005) illustrates that the selectively enhanced settling velocity due to air turbulence could make droplets grow rapidly from 20 to 80 µm and that this mechanism does not depend on the level of cloud turbulence. These studies, however, are based on turbulent collection kernels derived from either approximate or empirical formulations of the air turbulence and/or the motion of cloud droplets and, consequently, should be treated as primarily being qualitative.…”

Integrating biomass, sulphate and sea-salt aerosol responses into a microphysical chemical parcel model: implications for climate studies

“…In current models, the cloud droplets are prescribed with still air settling speeds. In reality, clouds are turbulent and when cloud droplets settle past microscale eddies inherently present in turbulent clouds, recent calculations show that droplets with radii approximately 10 mm do indeed settle faster than their still air fall speeds (Davila & Hunt 2001;Ghosh et al 2005a). Rogers & Yau (1989) suggest that autoconversion will only proceed once the number concentration of cloud droplets greater than 20 mm in radius exceeds approximately 10 3 m…”