A simplified mantle convection model for thermal conductivity stratification

Some important features characterizing thermal convection such as average temperature, Nusselt number and cooling rate are dominantly controlled by vertical thermal conductivity variations, although temperature-dependent thermal conductivity with lateral and vertical variations plays an important role in thermal convection of the Earth. It is therefore important to investigate the influence of depth-dependent thermal conductivity on mantle convection and thermal evolution. In this paper, we have employed a simplified two-layer conductivity model and studied the effects of depth-dependent thermal conductivity on convection by using both 2D numerical and 1D quasi-analytical models. First, numerical experiments including the two-layer conductivity models have been performed by using 2D Boussinesq convection models with an infinite Prandtl number. In these models, the distributions of thermal conductivity are simplified into a series of two-layered models, instead of using Hofmeister's full temperature and pressure-dependent model (1999, 2001). Various depths have been applied to separate the two contrasting thermal conductivities. Secondly, 1D loop models have been developed to compare the results found by 2D numerical experiments. In the loop models, different heat transfer coefficients have been introduced to the horizontal pipes for mimicking the 2D models. We have considered the behaviors of plume temperatures and flow rates in loop models for the different heat transfer coefficients. Decreasing the thermal conductivity with depth causes a weakened convection, whose Nusselt number, averaged temperature and averaged stream function are lower. On the other hand, increasing the thermal conductivity with depth produces stronger convection. In the cases with a decreasing thermal conductivity, the fluid cools more slowly because of the weakened heat transfer from the bottom. These results are consistent with those obtained by the 2D models. Our results also imply that the particular values of thermal conductivity in the horizontal thermal boundary layers at both ends of the mantle can exert more significant influence on convection than the thermal conductivity values in the mantle interior.