An idealized eddy-diffusivity model of entrainment mixing and evaporation is presented consisting of a continuous Eulerian relative humidity field and discrete Lagrangian droplets. Lagrangian droplet trajectories are calculated using a Brownian motion with commensurate diffusivity and a Lagrangian velocity decorrelation that is consistent with turbulent mixing. Using this new model, we revisit Jensen and Baker (1989)'s (JB) classic study of inhomogeneous mixing. Analysis of the governing dynamical and microphysical equations for the simplified geometry used by JB indicates that droplet spectral dispersion is a function of only three parameters: the ratio of the mixing and droplet evaporation timescales (the Damk?hler number, Da), the fraction of entrained air and the critical entrainment fraction that produces a cloudless but saturated well-mixed final state. These dependencies are encapsulated in four invariance theorems for isobaric mixing and evaporation that we derive and that establish a set of self-similar solutions for general entrainment scenarios that include sedimentation. A comparison of the predictions of our new model with JB's results verifies the acknowledged “homogeneous evaporation bias” in their model formulation and the exclusion of the large Da limit in JB's study. A full investigation of the JB entrainment scenario using our new model reveals a transition from homogeneous to inhomogeneous mixing in the droplet spectral dispersion at Da ≈ 5 and extreme inhomogeneous mixing behavior in the limit Da → ∞. The PDFs of the time-integrated Lagrangian subsaturation, int, in the inhomogeneous regime are observed to asymptote to a int ?1 law; implications of this finding for subgrid cloud modeling are discussed.
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