Approximate Models for Variable Density Fluid Motions

Abstract

This chapter aims at giving a comparative overview of some of the various models which, derived from the general Navier-Stokes equations, account for density variations according to several types of approximations. The role of the pressure is first examined. The Helmholtz decomposition is introduced and the linear analysis of Kovasznay compressible modes is presented. Then several models are discussed, referring to Boussinesq’s approximation, and other approximations which are concerned with (i) filtering acoustic effects, (ii) incorporating density variations in pseudo-incompressible formulations and (iii) deriving weakly compressible limits to the general compressible equations.