A comparison of incompressible, anelastic and Boussinesq dynamics

A comparative study of the incompressible and anelastic approximations is presented, including an energy budget analysis. The pure incompressible system for liquids and Durran's pseudo-incompressible system for gases decouple density from pressure fluctuations and thereby eliminate acoustic modes. The traditional Boussinesq incompressible and the Ogura-Phillips anelastic systems require linearization of the pressure-buoyancy terms in the equation of motion about a state of neutral static stability. This linearization is their principal merit but it costs accuracy, especially for strongly stratified or diabatic flows. By subtracting mean hydrostatic terms, disturbance forms of the pure incompressible and pseudo-incompressible equations of motion can be constructed, which allow a more uniform scaling of terms than the original equations but are not linearized. Conservative energy budget relations are derived for all the systems described.