A theory for convection should provide us with , among others, scaling for the convective available potential energy (CAPE), vertical velocity, buoyancy and fractional area covered by updrafts. Although such theory exists for dry convection, it is still missing for moist convection. To progress in this direction, we analyze the entropy budget of a convective atmosphere to derive the mechanical energy generated by convection and use this to constrain CAPE. This theory is then tested in numerical experiments with a high resolution Clouds Ensemble Model.
The entropy budget of an atmosphere in radiative-convective equilibrium is characterized by the balance between a large-scale entropy sink associated with the differential atmosphere and an entropy source due to the various irreversible phenomena occuring at the molecular level. For a dry atmosphere, frictional heating is the main irreversible entropy source. In this case, the analysis of the entropy budget allows to directly estimate the rate of production of mechanical energy from the distribution of heat sources and sinks. However, for a moist atmosphere, we demonstrate that the moistening of dry air, i.e. evaporation in unsaturated air and diffusion of water vapor, is the dominant irreversible entropy source. The mechanical work produced by the system can still be determined from the entropy budget but this requires to account properly for the moistening effect. As a result, moist convection generates much less mechanical work than dry convection for the same distribution of heat source and sinks.
Once the total mechanical energy production and the convective mass flux are determined, it is possible to estimate the average value of CAPE. We discuss then the dependency of CAPE on various parameters such as surface temperature, radiative cooling profile and precipitation efficiency. We also analyze the relationship between CAPE and vertical velocity, and show that the latter depends critically on whether frictional heating in the atmosphere results from a turbulent cascade to small scales or is associated with falling precipitation.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics