Instabilities of a buoyancy-driven system

Abstract

A buoyancy-driven system can be unstable due to two different mechanisms—one mechanical and the other involving buoyancy forces. The mechanical instability is of the type normally studied in connexion with the Orr-Sommerfeld equation. The buoyancy-driven instability is rather different and is related to the ‘Coriolis’-driven instability of rotating fluids. In this paper, the stability of a buoyancy-driven system, recently called a ‘buoyancy layer’, is examined for the whole range of Prandtl numbers, s. The buoyancy-driven instability becomes increasingly important as the Prandtl number is increased and so particular interest is attached to the limit in which the Prandtl number tends to infinity. In this limit, the system is neutrally stable to first order, but second-order effects render the flow unstable at a Reynolds number of order σ-½. Consequences of the results for the stability of convection in a vertical slot are examined.