Idealized Cumulus Cloud-Scale Motions and the Dynamics of Isolated and Coupled Flows
Developing an understandable theory for the dynamic evolution of the morphology of clouds remains intractable. To break this deadlock, we introduce a new conceptual model for cloud-scale motions named the Kinematics Representation of Non-rotating Updraft Tori (KRoNUT) model, where non-rotating reflects the absence of motion in the azimuthal direction. Using this model, we conduct a series of relaxation experiments whereby we ``turn off'' the baroclinic term associated with a pre-existing cloud-scale circulation. We then implement a moment reduction technique to generate a system of differential equations named the Dynamics of Non-rotating Updraft Tori (DoNUT) equations, which describe the temporal evolution of a cloudy circulation under various combinations of forcings, namely turbulent diffusion, self-advection, and cross-advection from a neighboring cloud-scale flow. The solutions of the DoNUT equations show that all single KRoNUT configurations either start at or evolve toward a specific steady state circulation. The cloud-scale motions represented by the current KRoNUT model always grow vertically but may narrow, due to advection, or widen, due to diffusion. Meanwhile, invigoration or enervation of the vertical velocity may result from advection or diffusion processes, with short, wide KRoNUTs more likely to invigorate and tall, narrow KRoNUTs likely to enervate. Our study of the coupled KRoNUTs provides insight into clouds' tendencies to attract or repel one another. Important results of the coupled KRoNUT analysis include a scaled metric for interaction, ranges of specific height ratios that induce the most meaningful interaction, and circulation parameters that alter the location and stability of a steady KRoNUT.