Rayleigh–Bénard convection

Rayleigh–Bénard convection is the buoyancy-driven flow of a fluid layer heated from below and cooled from above. When the temperature difference across the layer exceeds a critical value, the initially quiescent fluid becomes unstable and organized convection cells emerge. The phenomenon is named after Lord Rayleigh, who first analyzed the linear stability of the system in 1916, and Henri Bénard, who observed the cellular patterns experimentally in 1900.

The control parameter is the Rayleigh number, a dimensionless measure of the ratio of buoyancy forcing to viscous damping and thermal diffusion. Below a critical Rayleigh number (approximately 1708 for rigid boundaries), heat is transported by conduction alone and the fluid remains at rest. Above the critical value, the instability produces steady convection rolls, and at higher Rayleigh numbers the flow undergoes a sequence of bifurcations leading to increasingly complex dynamics — oscillatory convection, spatiotemporal chaos, and ultimately turbulence.

Rayleigh–Bénard convection is the canonical model system for the study of pattern formation, self-organization, and the transition to turbulence in dissipative structures. It is also the physical system that Edward Lorenz simplified to derive the Lorenz system and thereby discovered deterministic chaos.