The Oberbeck-Boussinesq Equations. The Stability of Constant Gradient Solutions of the Oberbeck-Boussinesq Equations

Abstract

The presence of density gradients in a fluid means that gravitational potential energy can be converted into motion through the action of buoyant forces. Density differences can be induced by heating the fluid and by forcing concentration differences in mixtures like salt water. In the Oberbeck-Boussinesq (OB) equations, the fluid is assumed to have a uniform density; density differences are recognized only in those terms which drive the motion. The OB equations are given in § 54. In § 55 we discuss boundary conditions of various kinds and complete the statement of the initial-boundary-value problem, IBVP, for the OB equations.