Introduction

Thermal instability often arises when a fluid is heated from below. The classic example of this, described in this chapter, is a horizontal layer of fluid with its lower side hotter than its upper. The basic state is then one of rest with light fluid below heavy fluid. When the temperature difference across the layer is great enough, the stabilizing effects of viscosity and thermal conductivity are overcome by the destabilizing buoyancy, and an overturning instability ensues as thermal convection. This convective instability may be distinguished from free convection, such as that due to a hot vertical plate, for which hydrostatic equilibrium is impossible. Again, a basic flow of free convection may itself be unstable. Our concern here with convection is only with thermal instability. Convective instability seems to have been first described by James Thomson (1882), the elder brother of Lord Kelvin, but the first quantitative experiments were made by Bénard (1900).

Rayleigh (1916a) wrote that