The 'effective buoyancy' of an accelerating parcel is its Archimedean buoyancy minus an offset, due to the parcel having to push some of the environmental fluid out of its way. This offset grows dramatically with parcel aspect ratio, so that parcels that are much wider than they are tall (such as GCM grid cells) hardly accelerate at all. Furthermore, this offset is enhanced when parcels are near the surface rather than aloft. By solving the relevant Poisson equations, we found analytical solutions which quantify both these effects (see figure left).
Effective Buoyancy, Inertial Pressure, and Convective Triggering
The other force besides effective buoyancy acting on convecting parcels is the inertial (or dynamic) pressure force. In tropical deep convection, most new convection is generated on the edges of 'cold pools' of air produced by evaporation of rain from existing convection. (A large cold pool is visible in the B field in the figure to the right, and the triggered convection along its edge is visible in the w field). It had long been thought that inertial pressure was responsible for this triggering, but the results of Tompkins (2001) suggested that effective buoyancy might also contribute. We helped settle this question by numerically solving the Poisson equations for both effective buoyancy and inertial acceleration in a simulation of tropical convection, showing that indeed the inertial acceleration dominates (bottom row of figure).
See Jeevanjee and Romps (2015) for details.
Simulations of tropical convection can spontaneously develop large-scale circulations even in the absence of any large-scale forcing, in a phenomenon known as "self-aggregation". This large-scale circulation partitions the atmosphere into moist and dry regions, as can be seen in the individual panels to the left. Such self-aggregation had previously only been seen in simulations with a domain larger than ~ 300 km on a side, but by disabling cold pools in our simulation, we obtained aggregation at all domain sizes (see figure).
See Jeevanjee and Romps (2013) for details.