Rayleigh–Bénard Convection — Critical Rayleigh Modes

Fluid heated from below becomes unstable at Ra_c = 1707.76 (free-slip boundaries). Above this threshold, rolls form with critical wavenumber k_c = π/√2. Simulate 2D convection via stream-function vorticity, visualizing temperature field and velocity rolls.

Rayleigh RaRa = 2000
Prandtl PrPr = 1.0
Aspect ratioΓ = 2
Ra_c = 1707.76 | k_c = π/√2 ≈ 2.22