Rayleigh-Bénard Convection Rolls

Thermal convection patterns driven by buoyancy above the critical Rayleigh number

Rayleigh Number

1708
Ra = gαΔT·h³ / (νκ)  |  Rc = 1708

Parameters







Physics

Ra = gαΔTh³/(νκ)

When Ra exceeds the critical value Rc ≈ 1708, a quiescent fluid layer heated from below becomes unstable to convective overturning. Hot fluid rises (red), cool fluid sinks (blue), forming regular rolls. The aspect ratio of rolls at onset is fixed by the critical wavenumber kc·h = π/√2.