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

Olivier Pauluis, Jörg Schumacher

Research output: Contribution to journalArticle

Abstract

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
Volume8
Issue number1
StatePublished - 2010

Fingerprint

Linear equations
Equations of state
Equation of State
Rayleigh
Piecewise Linear
Convection
Linear equation
Latent heat
Thermodynamics
Phase Transition
Air
Heat
Phase transitions
Atmospheric density
Boussinesq System
Atmospheric temperature
Local Equilibrium
Piecewise Linear Function
Thermodynamic Equilibrium
Water Vapor

Keywords

  • Atmospheric dynamics
  • Clouds
  • Convection

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Idealized moist Rayleigh-Bénard convection with piecewise linear equation of state. / Pauluis, Olivier; Schumacher, Jörg.

In: Communications in Mathematical Sciences, Vol. 8, No. 1, 2010, p. 295-319.

Research output: Contribution to journalArticle

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