Thermal convection cells, critical Rayleigh number, and Nusselt number scaling
Parameters
Ra = gαΔT h³/(νκ)
Ra_c = 1707.76 (critical onset)
Nu ~ Ra^(1/3) (turbulent)
Ra = 5000
Nu ≈ —
State: conduction
Convection onset at Ra_c ≈ 1708 (horizontal layer).
Near onset: Nu−1 ~ (Ra/Ra_c−1)^β.
Turbulent regime: Nu ~ Ra^(2/7) (Kraichnan) or Ra^(1/3) (GL theory).
The 2D simulation uses simplified Boussinesq equations with a pseudospectral-like approach.