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 incompres sible system for liquids and Durran's pseudo-incompressible system for gases decouple density from pressure fluctuations and thereby elimina te acoustic modes. The traditional Boussinesq incompressible and the O gura-Phillips anelastic systems require linearization of the pressure- buoyancy terms in the equation of motion about a state of neutral stat ic stability. This linearization is their principal merit but it costs accuracy, especially for strongly stratified or diabatic flows. By su btracting mean hydrostatic terms, disturbance forms of the pure incomp ressible and pseudo-incompressible equations of motion can be construc ted, which allow a more uniform scaling of terms than the original equ ations but are not linearized. Conservative energy budget relations ar e derived for all the systems described.