An incompressibility approximation is formulated for isentropic motions in a compressible stratified fluid by defining a pseudo density ?* and enforcing mass conservation with respect to ?* instead of the true density. Using this approach, sound waves will be eliminated from the governing equations provided ?* is an explicit function of the space and time coordinates and of entropy. By construction, isentropic pressure perturbations have no influence on the pseudo-density.
A simple expression for ?* is available for perfect gases that allows the approximate mass conservation relation to be combined with the unapproximated momentum and thermodynamic equations to yield a closed system with attractive energy conservation properties. The influence of pressure on the pseudo-density, along with the explicit space-time dependence of ?* is determined entirely by the hydrostatically balanced reference state. Methods for the efficient numerical integration of the pseudo-incompressible equations are discussed.