Rayleigh-Bénard Convection

Rayleigh-Bénard Convection: When a fluid layer is heated from below and cooled from above, buoyancy drives instability. The Rayleigh number Ra = αgΔTd³/(νκ) governs the balance between buoyancy (destabilizing) and thermal diffusion + viscosity (stabilizing). Below Ra_c ≈ 1708 (Rayleigh 1916), heat conducts without flow. Above Ra_c, convection rolls spontaneously appear. The pattern wavelength is ~2d at onset. At high Ra, the flow becomes turbulent. This simulation uses a simplified 2D model coupling temperature advection-diffusion to velocity via buoyancy, rendered as a color field (blue=cold, red=hot).