  Raylaigh-Benard convection is one of the most well-studied models in fluid
mechanics. Atmospheric convection, one of the most important components of the
climate system, is by comparison complicated and poorly understood. A key
attribute of atmospheric convection is the buoyancy source provided by the
condensation 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 the
Boussinesq limit of the ideal gas equations and adding a condensate that obeys
a simplified Clausius--Clapeyron relation. The system allows moist convection
to be explored at a fundamental level and reduces to the classical
Rayleigh-Benard model if the latent heat of condensation is taken to be zero.
The model has an exact, Rayleigh-number independent `drizzle' solution in which
the diffusion of water vapour from a saturated lower surface is balanced by
condensation, with the temperature field (and so the saturation value of the
moisture) determined self-consistently by the heat released in the
condensation. This state is the moist analogue of the conductive solution in
the classical problem. We numerically determine the linear stability properties
of this solution as a function of Rayleigh number and a nondimensional
latent-heat parameter. We also present a number of turbulent solutions.
