Buoyancy-Driven Flow

Physics: Rayleigh number Ra = gβΔTL³/(νκ), where β is thermal expansion coefficient, ν kinematic viscosity, κ thermal diffusivity. Onset of convection in a horizontal layer occurs at Ra ≈ 1708 (Rayleigh-Bénard instability). In the turbulent regime Nu ~ Ra^(1/3), relating heat flux to temperature difference. Prandtl number Pr = ν/κ sets the relative thickness of velocity and thermal boundary layers. Geothermal convection (Ra ~ 10⁷) drives plate tectonics; the sun's convection zone spans 200,000 km.