A Rigorous Exposition of the Boussinesq Approximations Applicable to a Thin Layer of Fluid.

The Boussinesq system of hydrodynamic equations applicable to a thin layer of fluid is rigorously developed from the Navier-Stokes equations and thermodynamic equation. The Boussinesq system is shown to be valid if two independent, non-dimensional parameters E and E3 are sufficiently small. If a' is the coefficient of volume expansion; K0, the thermal diffusivity; C0, the specific heat at constant pressure; e', a characteristic temperature difference; and L' a characteristic length; then Ei a'O' and K,'2/C0L'2O'. By expanding the general energetic equations in a power series in El and E2, the Boussinesq energetics are completely clarified.