Towards a similarity theory of moist convective updrafts

The mixing of air between clouds and their environment is investigated with the help of a simplified model problem that contains only a small number of dynamically relevant parameters, whose influence can be systematically explored. The classical model of a buoyant thermal, extensively studied in laboratory experiments, is generalised to include the key moist processes of condensation and reevaporation of cloud water. We consider the evolution of an isolated thermal initiated from a spherical warm and moist bubble at rest in a moist neutral sounding. The moist thermal loses buoyancy through mixing with the unsaturated environmental air, and finally collapses. The effect of moist physics on the thermal is shown to be represented by only three scale-independent parameters. As is expected for real clouds, these thermals do depend on their initial conditions, and therefore are not self-similar. However, we present large eddy simulations that exhibit an approximate dynamical similarity, in that the loss of buoyancy resulting from the mixing process is mainly described by a single scale-invariant parameter which we call the effective buoyancy, B_eff. In order for the thermal to ascend a distance significantly larger than its initial diameter, B_eff must be much greater than unity. This implies that the environment must be close to saturation if the bubble has an initial buoyancy that is typical of real clouds. It is also shown that the stratification of the environment induces a length scale, L_buo, for a thermal with a given buoyancy excess. The resulting scale-independent parameter L_eff=L/L_buo (where L is the initial bubble radius) is shown to affect the geometry of the thermal. Indeed, the thermal may break up if L_eff is too large. These geometrical effects can be explained by relating L_buo to the depth reached by forced downdrafts, which corresponds to the vertical extent of the largest eddies that entrain unsaturated air into the thermal.