A tubulent diffusive model for atmospheric moist convection

In the ocean, convection and plume formation occur when a fluid parcel at the ocean’s surface becomes heavier than its environment. Switching to convection in a dry atmosphere involves two main variations: a sweap over of the vertical direction, with light plumes propagating up from the ground, and a more subtle definition of what it means for an air parcel to be light. In comparing the buoyancy of two parcels of a compressible fluid at different pressures, it is the entropy difference, not the density, that matters. When moving into a less pressurised environment, a parcel expands, so its density decreases, but its entropy remains constant, provided that the expansion is adiabatic (i.e., slow in comparison with the adjustment time to thermodynamical equilibrium, and with no heat exchange between the parcel and its surroundings.) Hence a vertical profile neutrally stable to convection is one of constant entropy, with a corresponding lapse rate of about ten degrees Celcius per kilometer. This situation changes quite significantly when the air has some moist –i.e., water vapor– content. When this is the case, as a rising parcel expands and cools, it may reach a point at which its vapor content exceeds saturation. When the excess water condensates, it releases latent heat, which further expands the parcel, providing an extra push up often capable of turning unstable to convection, density profiles that would be stable under dry conditions. Indeed, the lapse rate for saturated air is reduced by nearly fifty percent, to about five degrees Celcius per kilometer. This moist convective instability is highly asymmetric: air that descends, and hence contracts and warms up, departs from saturation. Thus the lapse rate for descending moist air is the same as for dry air, even though the one for ascending air is much decreased. As a consquence, warm moist air tends to ascend in rapid, small–scale plumes, while subsiding air, driven not by instability but by global mass conservation, descends much more slowly and over extended areas. The paragraphs above provide a qualitative description of the nature of moist convection. Switching to a more quantitative model, where one may study complex dynamics, such as the interactions among convective cells, or the effects of