Rayleigh-Bénard Convection

Thermal plumes, Nu-Ra scaling, turbulent Prandtl boundary layers

Ra: 10⁵
Pr: 0.71
Nu: —
t: 0
Rayleigh-Bénard convection: hot bottom plate, cold top plate. Ra = gβΔTL³/(νκ). Below Rac ≈ 1708: pure conduction. Above: rolls form (Nu > 1). Turbulent regime: Nu ~ Ra2/7 (Castaing 1989) or Ra1/3 (ultimate regime). The Prandtl number Pr = ν/κ controls whether viscous or thermal boundary layers dominate. Plumes carry heat through the bulk; boundary layers control transport.