Correlation of Cloud Droplet Growth with the Scalar Fluctuations in a Turbulent Moist Convection

Cloud droplet growth in a turbulent environment is studied by creating turbulent moist Rayleigh-B{\'e}nard convection in the Michigan Tech Pi Chamber. Cloud formation is achieved by injecting aerosols into the water-supersaturated environment created by the isobaric mixing of saturated air at different temperatures. A range of steady-state cloud droplet number concentration is achieved by supplying aerosols at different rates. As steady-state droplet number concentration is decreased the mean droplet size increases as expected, but also the width of the size distribution increases. This increase in the width is associated with larger supersaturation fluctuations due to the slow droplet microphysical response (sink of the water vapor) compared to the fast turbulent mixing (source of the water vapor). The observed standard deviation of the squared droplet radius is a linear function of the combined time scale of the system $\tau_s^{-1} = \tau_c^{-1} + \tau_t^{-1}$; here, $\tau_c$ is the phase relaxation time and $\tau_t$ is the turbulence correlation time. A stochastic differential equation approach for supersaturation also predicts the same linear response. This finding has significance for cloud-radiation budgets and precipitation formation.