Convection, Stability and Turbulence

Many natural flows are driven by buoyancy forces, perhaps the most familiar being those resulting from density variations due to temperature differences in the presence of a gravitational field. The simplest setting to study this sort of system is so-called Rayleigh-Bénard convection, the buoyancy driven flow in a horizontal layer of fluid heated from below and cooled from above. This seminal problem has received tremendous theoretical and experimental attention over the last century but many riddles remain, especially for buoyancy-driven turbulent transport. Following an introduction to the phenomena and its applications along with a review of the current state of theory and experiments on turbulent Rayleigh-Bénard convection, I will describe some of the light that mathematical analysis has shed on the subject in recent years.