Rayleigh-Bénard Convection

Convection rolls forming above the critical Rayleigh number Ra_c ≈ 1708

Rayleigh-Bénard convection occurs when a fluid layer is heated from below. Above the critical Rayleigh number Ra_c = 1708 (for free-slip boundaries), the conductive state becomes unstable and convection rolls spontaneously form. The Rayleigh number Ra = gαΔTd³/(νκ) balances buoyancy against viscous and thermal diffusion.