Convection in a compressible fluid

Abstract

In section 3.2 we have discussed the Boussinesq approximation for the equations of thermal convection in a linear viscous fluid. The equations arising from the Boussinesq approximation, (3.41), have been extensively employed in this book. However, there are situations in which compressibility effects are important, or one wishes to study convection in a very deep layer. In these circumstances, the Boussinesq approximation is generally believed to be inappropriate. In this chapter we examine some of the models which have been employed to take account of compressibility effects or convection in a deep layer. We begin in this section with an energy analysis of two models for thermal convection in a deep layer.