Slippery Thermals and the Cumulus Entrainment Paradox*

Abstract In numerical simulations of growing congestus clouds, the maximum upward velocities w typically occur in compact toroidal vortices or thermals. These maxima were tracked, and the momentum budget was analyzed within spherical regions centered on them with objectively determined radii approximately enclosing the vortex ring or pair. Such regions are proposed as an advantageous prototype for rising air parcels due to their prolonged identity as evident in laboratory flows. Buoyancy and other forces are generally less than 0.02 m s−2 (0.7 K). In particular, resolved mixing between thermals and their environment fails to produce the drag normally anticipated, often producing even a slight upward force, indicating that parcel models should allow for significantly different dilution rates for momentum than for material properties. A conceptual model is proposed to explain this as a result of the thermals' internal circulation and detrainment characteristics. The implications of momentum dilution for cumulus development are explored using a simple model of a heterogeneous entraining parcel. Without friction, parcels reach the upper troposphere even at a high entrainment rate [~(2 km)−1] if the environment is sufficiently humid, whereas with standard momentum dilution, a much lower entrainment rate is required. Peak condensed water amounts and sensitivities of cloud amount and height to ambient humidity are significantly more realistic in the high-entrainment case. This suggests that revised treatments of friction and momentum could help address the “entrainment paradox” whereby entrainment rates implied by detailed cloud studies are higher than those typically preferred for parcel-based calculations.