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The impact of turbulent mixing on the droplet size distribution is studieddeep inside a warm ice-free cloud. A simplified cloud mixing model wasimplemented therefore which summarizes the balance equations of water vapormixing ratio and temperature to an effective advection-diffusion equation forthe supersaturation field $s(\textbf{x},t)$. Our three-dimensional directnumerical simulations connect the scalar supersaturation field to the clouddroplet dynamics, in particular to the droplet size distribution for differentbox sizes. In addition, finite-time Lyapunov exponents are monitored such thatwe can relate regions of higher compressive strain to those of high localsupersaturation amplitudes. We find that the mixing process in terms of thedroplet evaporation is always homogeneous in the bulk of the cloud, while beinginhomogeneous in view to the relaxation of the supersaturation field. Theprobability density function of $\lambda_3$ is related to the one of $s$ by asimple one-dimensional aggregation model. The distributions of the compressivefinite-time Lyapunov exponents $\lambda_3$, the supersaturation field, and thedroplet size are found to be Gaussian.

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