Rayleigh–Bénard Convection Rolls

Thermal instability driven by buoyancy: Ra = gαΔTd³/νκ > Ra_c ≈ 1708

Parameters

Physics

Ra/Ra_c
Nusselt Nu
Regime
Ra = gαΔTd³/(νκ) — buoyancy vs diffusion
Ra_c ≈ 1708 (onset of convection)
Critical wavenumber k_c = π/√2
Nu ≈ 0.069 Ra^{1/3} Pr^{-2/7} (turbulent)
Lorenz equations → chaos at Ra≫Ra_c