Self-aggregation of moist convection in a conditionally unstable environment

Conditionally unstable convection occurs when the stratification is stable for unsaturated air parcels but unstable for saturated air parcels. This leads to the development of isolated convective plumes separated by unsaturated dry environment. In this paper, the statistical behavior of conditionally unstable convection is studied in a model of moist turbulent convection with a simplified thermodynamics of cloudy air. It is closely related to the classical Rayleigh-Benard problem, but includes phase transitions between the gaseous and liquid phase and the effect of latent heat release on the buoyancy of air parcels. In practice, phase transition results in a discontinuity of partial derivatives with respect to thermodynamic state variables at the phase boundary. The advantage of this model is that it becomes readily accessible to mathematical investigation and direct numerical simulations of turbulence. Since all flow scales down to the viscous Kolmogorov scale are resolved, the accessible Rayleigh numbers remain moderate. We demonstrate that this simplified model is not only capable to simulate cloud formation processes, but also indicates that the complex dynamics of moist convection results in the emergence of new convective regimes that do not exist in the absence of phase transition.

In this study, we show that, for small aspect ratios, convection is highly intermittent, with intense convective burst separated by long quiescent interval. At larger aspect ratios however, self-sustained convective regimes are observed in which isolated turbulent cloud aggregates are surrounded by ambient regions of slowly descending unsaturated air. The transition to self-aggregated convection is however highly sensitive to the diffusivity and viscosity used in the model, with the aspect ratio necessary for the transition increasing as the viscosity and diffusivity are decreased. In addition, it is also found that conditionally unstable moist convection is inefficient at transporting energy. It is argued here that this weak energy transport is tied to the presence of a diffusive layer near the lower boundary, which remains present even when the diffusivity is small.

We also investigate the impacts of radiative cooling on the self-sustained convective regimes. It is found that the addition of a small bulk radiative cooling leads to the emergence of a shallow convectively unstable layer near the lower boundary. This results in significant increases of convective activity, kinetic energy generation and upward energy transport across the entire atmosphere.