Rayleigh-Bénard convection in Earth's mantle — Ra = αgΔTd³/νκ
Ra = αgΔTd³ / (νκ)
α = thermal expansivity (~3×10⁻⁵ K⁻¹)
ΔT = temperature contrast (~2500 K)
d = layer thickness (2900 km whole mantle)
ν = kinematic viscosity (~10¹⁷ m²/s)
κ = thermal diffusivity (~10⁻⁶ m²/s)
Earth's mantle Ra ≈ 10⁶–10⁸. Critical Ra_c ≈ 1100.
The 660-km discontinuity (ringwoodite→bridgmanite+periclase) is a phase transition. Seismic tomography shows slabs penetrating it (implying whole-mantle flow), yet a compositional density difference may cause layered convection intermittently — an ongoing debate.