Rayleigh-Bénard Convection

Rayleigh-Bénard convection occurs when a fluid layer heated from below reaches the critical Rayleigh number Ra_c ≈ 1708 (for rigid-rigid boundaries). Below this threshold buoyancy cannot overcome viscous dissipation and heat diffuses conductively. Above Ra_c, convection rolls form with wavenumber k_c = π/√2. The Prandtl number Pr = ν/κ (viscosity / thermal diffusivity) controls roll geometry. At high Ra, rolls become time-dependent, then chaotic (hard turbulence). Visualization shows temperature field (red=hot, blue=cold) and streamlines of the velocity field.