On the Problem of Multivalued Pressure in the Theory of Convection

Abstract

In the theory of convection, pressure is governed by a diagnostic partial differential equation which for appropriate boundary conditions does not have a unique solution. While from a dynamic point of view this may be of little consequence, it can be of importance in the thermodynamics where pressure and other state variables occur undifferentiated. In this note it is shown that by consistent use of kinematic and thermodynamic constraints, the pressure can be made unique.