On the Boussinesq approximation and its role in the theory of internal waves

Abstract

Most studies of the dynamics of fluids with weak density gradients use the Boussinesq approximation, which neglects density variations in the inertial terms of the equation of motion. The significance of this approximation is investigated here. As a general matter, it appears that care is called for in the use of the approximation if quantities other than the non-dimensional density difference are small. Also, the existence of certain phenomena of interest and importance may depend on the small terms neglected by the Boussinesq approximation. This is shown by an investigation of solitary waves in a stratified fluid system.