Idealized moist Rayleigh-Bénard convection with piecewise linear equation of state

Olivier Pauluis, Jörg Schumacher

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)295-319
Number of pages25
JournalCommunications in Mathematical Sciences
Issue number1
StatePublished - 2010


  • Atmospheric dynamics
  • Clouds
  • Convection

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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