Representation of turbulent mixing and buoyancy reversal in bulk cloud models

This paper discusses the representation of subgrid-scale turbulent mixing in bulk models of warm (ice free) clouds, which assume instantaneous adjustment to grid-scale saturation. This is a reasonable assumption for condensation of water vapor because supersaturations inside clouds are typically small (∼0.1% or smaller), except near cloud bases where about an order of magnitude larger supersaturations are anticipated. For the cloud evaporation, however, instantaneous adjustment to grid-scale saturation is questionable, especially when evaporation occurs as a result of turbulent mixing between a cloud and its unsaturated environment. This is because turbulent mixing between initially separated volumes of cloudy and cloud-free environmental air proceeds through a gradual filamentation of these volumes, with progressively increasing evaporation of cloud water during the approach to final homogenization. A relatively simple model of this chain of events is included in a bulk model of moist nonprecipitating thermodynamics. The model delays adjustment to saturation for cloud evaporation following the turbulent mixing until the volume can be assumed homogeneous. An additional prognostic variable, the width of a cloudy filament, is added to represent the progress of turbulent mixing and the approach to homogenization. Theoretical developments are illustrated by idealized 2D simulations of moist thermals rising from rest and realistic large-eddy simulations of a cloud field.