Thermal convection rolls: onset at Ra = Ra_c ≈ 1708
2000
7.0
3.0
4
Ra / Ra_c
1.17
Regime
Convection
Nu (Nusselt)
—
Rayleigh–Bénard convection occurs when a fluid layer heated from below becomes unstable at Ra_c ≈ 1708 (for rigid boundaries). Below this, heat transfers purely by conduction. Above Ra_c, convection rolls appear — a supercritical pitchfork bifurcation. The wavenumber at onset is k_c ≈ 3.12. Nu ≈ 1 + A(Ra/Ra_c - 1) near onset; for large Ra, Nu ~ Ra^(2/7). Colors show temperature (red=hot, blue=cold); arrows show velocity field.