Time-dependent modeling of oscillatory instability of three-dimensional natural convection of air in a laterally heated cubic box

Abstract

Transition from steady to oscillatory buoyancy convection of air in a laterally heated cubic box is studied numerically by straight-forward time integration of Boussinesq equations using a series of gradually refined finite volume grids. Horizontal and spanwise cube boundaries are assumed to be either perfectly thermally conducting or perfectly thermally insulated, which results in four different sets of thermal boundary conditions. Critical Grashof numbers are obtained by interpolation of numerically extracted growth/decay rates of oscillation amplitude to zero. Slightly supercritical flow regimes are described by time-averaged flows, snapshots, and spatial distribution of the oscillation amplitude. Possible similarities and dissimilarities with two-dimensional instabilities in laterally heated square cavities are discussed. Break of symmetries and sub- or supercritical character of bifurcations are examined. Three consequent transitions from steady to the oscillatory regime, from the oscillatory to the steady regime, and finally to the oscillatory flow, are found in the case of perfectly insulated horizontal and spanwise boundaries. Arguments for grid and time-step independence of the results are given.