Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: Solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time-dependent Boussinesq equations is reported.