Mantle dynamics with pressure- and temperature-dependent thermal expansivity and conductivity

Abstract

In numerical simulations of mantle convection it is commonly assumed that the coefficients of thermal expansion α and thermal conduction k are either constant or pressure-dependent. Pressure changes are generally computed using parametrizations that rely on extrapolations of low-pressure data for a single upper-mantle phase. Here we collect data for both the pressure and temperature dependence of α from a database of first-principles calculations, and of k from recent experimental studies. We use these data-sets to construct analytical parametrizations of α and k for the major upper- and lower-mantle phases that can be easily incorporated into exisiting convection codes. We then analyze the impact of such parametrizations on Earth’s mantle dynamics by employing two-dimensional numerical models of thermal convection. When α is the only variable parameter, both its temperature and pressure dependence enhance hot plumes and tend to inhibit the descent of cold downwellings. Taking into account a variable k leads to a strong increase of the bulk mantle temperature, which reduces the buoyancy available to amplify bottom boundary layer instabilities and causes mantle flow to be driven primarily by the instability of cold plates whose surface velocity also tends to rise. When both parameters are considered together, we observe an increased propensity to local layering which favors slab stagnation in the transition zone and subsequent thickening in the lower mantle. Furthermore, the values of k near the core-mantle boundary ultimately control the effect of this physical property on convection, which stresses the importance of determining the thermal conductivity of the post-perovskite phase.