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

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 alpha 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 alpha, alpha(p ), alpha(T ) and alpha(p , T ) we find that at mantle temperatures the pressure dependence of alpha is important. For the lithosphere the dependence of alpha on temperature dominates, since the temperature dependence of alpha is much stronger in the low-pressure regime. Also dynamic topography changes considerably (up to 15 per cent) if alpha 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-alpha case by at most 12 per cent if an effective Rayleigh number based on the spatial average of alpha is used.