Inertial effects on recurrent pattern formation in periodically driven Rayleigh–Bénard convection

Periodically driven Rayleigh–Bénard convection is modelled by a vertical mode expansion of a mean field approximation to the Oberbeck–Boussinesq equations with thermal noise. The resulting model generalizes the Lorenz Model introduced by Ahlers, Hohenberg, and Lücke [Phys. Rev. A 32 (1985) 3493] including the continuous dependence on the horizontal wavenumber. The model is used to predict the order–disorder transition experimentally observed in the recurrent pattern formation near the convective onset, showing that the inclusion of inertial effects in the description of externally modulated pattern forming transitions, leads to theoretical predictions for the effects of thermal noise much closer to the experimental results than those of previous (purely dissipative) models.