Two-Dimensional Numerical Models of Mantle Convection

Abstract

This chapter describes the models of mantle convection that have been confined to two-dimensional plane layers in Cartesian coordinates. Scientific interest in the subject of thermal convection was stimulated initially by the detailed laboratory experiments of Bénard, who observed steady cellular convection in thin layers of viscous fluids. Overstable modes have been observed in studies of heated fluids that contain a stabilizing linear salt gradient and in chemically layered infinite Prandtl number fluids. However, once the basic physics involved is understood, the move from modeling physical processes to actually simulating global geological events will require fully three-dimensional numerical experiments. One obvious qualitative difference due to the change in geometry is the increased surface area of the upper boundary layer relative to the lower. This enables more sinking plumes to develop from the upper boundary as opposed to rising plumes developing from the lower boundary. Although, the horizontal spacing of plumes originating in top and bottom boundary layers is comparable, the angular order of the resulting lateral temperature variations is approximately doubled at the upper surface relative to the lower Solheim.