Three‐dimensional spherical models of layered and whole mantle convection

Abstract

We present numerical calculations of three‐dimensional spherical shell thermal convection for constant viscosity and stratified viscosity models of whole‐layer and two‐layer mantle convection. These four examples are intended to provide theoretical guidance for determining the style of convection that is occurring in Earth's mantle. An impermeable interface between the upper and lower converting shells in the two‐layer solutions is placed at a depth of 670 km to coincide with the mantle seismic discontinuity that divides the upper and lower mantle. The interface results in an internal thermal boundary layer that raises the mean temperature in the lower shell by about 1400 K compared to the whole‐layer solutions. The patterns of convection in the upper part of the whole‐layer solutions are dominated by narrow arcuate sheetlike downflows in a background of weak upflow. In contrast, the upper shells of the two‐layer solutions have complicated networks of convective rolls with the upflows and downflows having very similar structure. The structure of convection in the lower shells is similar to that in the lower part of the whole‐layer solutions. An increase (decrease) in the viscosity in the lower (upper) shell decreases (increases) the convective velocity in the lower (upper) shell and increases (decreases) the horizontal scale in the lower (upper) shell. The upper and lower shells are viscously coupled at the 670‐km interface when viscosity is the same in the two shells. However, when viscosity in the lower shell is 30 times greater than that in the upper shell, the coupling is partially viscous and partially thermal. Based on the horizontal structure of subduction zones on Earth's surface and on tomographic images of temperature variations in Earth's mantle, we conclude that the style of convection in Earth's mantle is more like that of the whole‐mantle models.