(Joint work with Yue-Kin Tsang) The dynamics of atmospheric water in all its forms (vapour, liquid and ice) is an essential ingredient of weather and climate. Water vapour, in particular, is a greenhouse gas whose distribution has a strong impact on climate. Although atmospheric water is an active tracer which affects the dynamics, some insight into the factors controlling its distribution can be gained by analysing simple kinematic models. In such models, water vapour is treated as a passive scalar that is advected by a prescribed flow and reacts through condensation. Condensation acts as a sink that maintains specific humidity below a prescribed, spatially dependent saturation value. Models of this type have been studied by Pierrehumbert and others using spatially decorrelated Brownian motion as a crude model of turbulent motion. In this work we examine the effect of a coherent flow represented by a single vortex which adds a deterministic component to the random motion of fluid parcels. We consider two problems: (i) the drying of a water-vapour anomaly released in the flow at an initial time, and (ii) the steady-state water-vapour distribution achieved in the presence of a moisture source at a boundary. For both problems, we focus on the limit of strong vortex and derive the distribution of fluid-parcel position and humidity using averaging and, for problem (ii), matched asymptotics. The results, confirmed by Monte Carlo simulations, exhibit realistic features such as bimodal humidity distribution and spatially concentrated rainfall.
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