Pressure- and temperature-dependent thermal expansivity and the effect on mantle convection and surface observables

Abstract

In most mantle convection studies with variable thermal expansivity only the pressure dependence is considered. Here we investigate the effect of temperature-and/or pressure-dependent thermal expansivity α on the distribution of buoyancy forces in mantle convection. Thermal expansivity is calculated for the dominant upper-mantle mineral, forsterite, and a map of its dependence on T and p is given. By studying simple 2-D steady-state constant-viscosity convection and comparing cases with constant α, α (p), α(p) and α(p,T) we find that at mantle temperatures the pressure dependence of α is important. For the lithosphere the dependence of α on temperature dominates, since the temperature dependence of α is much stronger in the low-pressure regime. Also dynamic topography changes considerably (up to 15 per cent) if α is T- and p-dependent compared with a constant or only p-dependent case. Scaling laws for the Nusselt number and the rms velocity are obtained. They differ from the constant-α case by at most 12 per cent if an effective Rayleigh number based on the spatial average of α is used.