Ra: 5000
Ra_c ≈ 1708
Nu: —
Max |v|: —
Step: —
Ra_c ≈ 1708
Nu: —
Max |v|: —
Step: —
Rayleigh-Bénard instability occurs when Ra > Ra_c ≈ 1708.
Ra = gαΔTd³/(νκ)
Critical wavenumber: k_c = π/√2
Nusselt number measures heat transport enhancement over pure conduction. Near onset: Nu − 1 ∼ (Ra − Ra_c)^β
Turbulent convection: Nu ~ Ra^(1/3) (hard turbulence).
Ra = gαΔTd³/(νκ)
Critical wavenumber: k_c = π/√2
Nusselt number measures heat transport enhancement over pure conduction. Near onset: Nu − 1 ∼ (Ra − Ra_c)^β
Turbulent convection: Nu ~ Ra^(1/3) (hard turbulence).