The Boussinesq approximation for buoyant flows

The aim of this paper is to present a simplified, yet rigorous, deduction of the Boussinesq approximated governing equations for buoyant flows. In order to carry out the core deduction procedure, a simplified version of the manifold asymptotic analyses available in the literature is discussed. The method adopted in this study is focussed on the local balance equations valid for a general, not necessarily Newtonian, fluid. The analysis is carried out by demonstrating the leading order terms in the governing equations for the asymptotic limit which characterises the approximation. The role played by the effect of viscous dissipation is also taken into account.