Rayleigh–Bénard Convection Rolls
Thermal instability driven by buoyancy: Ra = gαΔTd³/νκ > Ra_c ≈ 1708
Parameters
Rayleigh Ra =
5000
Prandtl Pr =
7.0
Number of rolls =
3
Simulation speed =
1.0
Pause
Physics
Ra/Ra_c
—
Nusselt Nu
—
Regime
—
Ra = gαΔTd³/(νκ) — buoyancy vs diffusion
Ra_c ≈ 1708 (onset of convection)
Critical wavenumber k_c = π/√2
Nu ≈ 0.069 Ra^{1/3} Pr^{-2/7} (turbulent)
Lorenz equations → chaos at Ra≫Ra_c