An idealized framework to study the impacts of phase transitions on atmospheric
dynamics is described. Condensation of water vapor releases a significant amount of latent heat,
which directly affects the atmospheric temperature and density. Here, phase transitions are treated
by assuming that air parcels are in local thermodynamic equilibrium, which implies that condensed
water can only be present when the air parcel is saturated. This reduces the number of variables
necessary to describe the thermodynamic state of moist air to three. It also introduces a discontinuity
in the partial derivatives of the equation of state. A simplified version of the equation of state is
obtained by a separate linearization for saturated and unsaturated parcels. When this equation of
state is implemented in a Boussinesq system, the buoyancy can be expressed as a piecewise linear
function of two prognostic thermodynamic variables, D and M, and height z. Numerical experiments
on the nonlinear evolution of the convection and the impact of latent heat release on the buoyant
flux are presented.