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The supersaturation local balance equation is considered at a cloud boundary, and the structure of its turbulent production term is inferred from numerical experiments. The transient decay of an unstable-stratified, shearless-mixing layer at a warm cloud top is modeled as an initial value problem, in which the turbulent velocity, the active scalars, and the droplet dynamics are solved concurrently. The evolution of the cloud-clear air interface and the droplets therein is investigated via direct numerical simulations. Both initial monodisperse and polydisperse droplet size distribution cases are treated. We attempt to model the turbulent production of supersaturation - defined as the difference between the time derivative of the supersaturation and the condensation terms - in the mixing layer. The planar averages of the supersaturation production term are clearly correlated with the planar covariance of the computed horizontal velocity derivative and supersaturation fields, thus suggesting that a quasi-linear relationship may exist between these quantities. The value of the non-dimensional proportionality constant is deduced by i) modeling the production term as the interaction of two sinusoidal perturbations with local and global small-scale frequencies, and ii) spatially averaging the production term and the covariance of the supersaturation and the longitudinal velocity derivatives. It has been verified that the value of such proportionality constant does not vary considerably throughout the transient decay and is not sensitive to the initial droplet distribution dispersity.