Connecting finite-time Lyapunov exponents with supersaturation and droplet dynamics in the bulk of a turbulent cloud

Abstract

The impact of turbulent mixing on the droplet size distribution is studied deep inside a warm ice-free cloud. A simplified cloud mixing model was implemented therefore which summarizes the balance equations of water vapor mixing ratio and temperature to an effective advection-diffusion equation for the supersaturation field $s(\textbf{x},t)$. Our three-dimensional direct numerical simulations connect the scalar supersaturation field to the cloud droplet dynamics, in particular to the droplet size distribution for different box sizes. In addition, finite-time Lyapunov exponents are monitored such that we can relate regions of higher compressive strain to those of high local supersaturation amplitudes. We find that the mixing process in terms of the droplet evaporation is always homogeneous in the bulk of the cloud, while being inhomogeneous in view to the relaxation of the supersaturation field. The probability density function of $\lambda_3$ is related to the one of $s$ by a simple one-dimensional aggregation model. The distributions of the compressive finite-time Lyapunov exponents $\lambda_3$, the supersaturation field, and the droplet size are found to be Gaussian.