Abstract
Abstract. In a laboratory cloud chamber that is undergoing Rayleigh–Bénard convection, supersaturation is produced by isobaric mixing. When aerosols (cloud condensation nuclei) are injected into the chamber at a constant rate, and the rate of droplet activation is balanced by the rate of droplet loss, an equilibrium droplet size distribution (DSD) can be achieved. We derived analytic equilibrium DSDs and probability density functions (PDFs) of droplet radius and squared radius for conditions that could occur in such a turbulent cloud chamber when there is uniform supersaturation. We neglected the effects of droplet curvature and solute on the droplet growth rate. The loss rate due to fallout that we used assumes that (1) the droplets are well-mixed by turbulence, (2) when a droplet becomes sufficiently close to the lower boundary, the droplet's terminal velocity determines its probability of fallout per unit time, and (3) a droplet's terminal velocity follows Stokes' law (so it is proportional to its radius squared). Given the chamber height, the analytic PDF is determined by the mean supersaturation alone. From the expression for the PDF of the radius, we obtained analytic expressions for the first five moments of the radius, including moments for truncated DSDs. We used statistics from a set of measured DSDs to check for consistency with the analytic PDF. We found consistency between the theoretical and measured moments, but only when the truncation radius of the measured DSDs was taken into account. This consistency allows us to infer the mean supersaturations that would produce the measured PDFs in the absence of supersaturation fluctuations. We found that accounting for the truncation radius of the measured DSDs is particularly important when comparing the theoretical and measured relative dispersions of the droplet radius. We also included some additional quantities derived from the analytic DSD: droplet sedimentation flux, precipitation flux, and condensation rate.
Highlights
In a laboratory cloud chamber, such as the chamber at Michigan Technological University (Chang et al, 2016), it is possible to produce Rayleigh–Bénard convection by applying an unstable temperature gradient between the top and bottom water-saturated surfaces of the chamber
Supersaturation is produced by isobaric mixing within the turbulent flow
When aerosols are injected at a constant rate, an equilibrium state is achieved in which the rate of droplet activation is balanced by the rate of droplet loss
Summary
In a laboratory cloud chamber, such as the chamber at Michigan Technological University (Chang et al, 2016), it is possible to produce Rayleigh–Bénard convection by applying an unstable temperature gradient between the top and bottom water-saturated surfaces of the chamber. The resulting equilibrium droplet size distributions (DSDs) have been extensively measured in the chamber, and theoretical models proposed for some aspects of the DSDs (e.g., Chandrakar et al, 2016, 2017; Chandrakar et al, 2018a, c; Saito et al, 2019), obtaining a complete quantitative theory for the equilibrium DSDs has been elusive The reasons for this include the difficulty of accurately measuring supersaturation in a cloud chamber (e.g., Chandrakar et al, 2016) as well as uncertainties in our knowledge of the physical processes that determine the DSD.
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