Cell pattern of thermal convection induced by internal heating

Abstract

A numerical simulation of thermal convection induced by internal heating in a three-dimensional thin flat box is performed. The upper boundary is held at a constant temperature and the lower boundary is thermally insulated with a uniform internal heating in a fluid layer. We observe hexagonal cells with downwelling at their center in moderate Rayleigh number (RaH≲30RaHc). As the Rayleigh number increases, the cell size increases. We also observe a pattern transition: sheet-like downwellings gradually develop around the columnar downwelling with increasing Rayleigh number. At ∼30RaHc, hexagonal cells with sheet downwelling at their center (spoke pattern) is observed. These sheets can be seen only near the upper boundary. At 30RaHc∼70RaHc, the cells experience successive transitions to the pattern which are dominated by sinking sheet.