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Raylaigh-Benard convection is one of the most well-studied models in fluidmechanics. Atmospheric convection, one of the most important components of theclimate system, is by comparison complicated and poorly understood. A keyattribute of atmospheric convection is the buoyancy source provided by thecondensation of water vapour, but the presence of radiation, compressibility,liquid water and ice further complicate the system and our understanding of it.In this paper we present an idealized model of moist convection by taking theBoussinesq limit of the ideal gas equations and adding a condensate that obeysa simplified Clausius--Clapeyron relation. The system allows moist convectionto be explored at a fundamental level and reduces to the classicalRayleigh-Benard model if the latent heat of condensation is taken to be zero.The model has an exact, Rayleigh-number independent `drizzle' solution in whichthe diffusion of water vapour from a saturated lower surface is balanced bycondensation, with the temperature field (and so the saturation value of themoisture) determined self-consistently by the heat released in thecondensation. This state is the moist analogue of the conductive solution inthe classical problem. We numerically determine the linear stability propertiesof this solution as a function of Rayleigh number and a nondimensionallatent-heat parameter. We also present a number of turbulent solutions.

A Simple System for Moist Convection: the Rainy-Benard Model