Parametrizing the thermal evolution of a convective mantle that becomes conductive

2-dimensional and 3-dimensional dynamical fluid flow simulations can resolve the thermo-physical processes that are most relevant for the thermal evolution of planetary mantles, but their high numerical costs make them impractical for investigating large parameter spaces. For this reason, 1-dimensional parametrized thermal evolution models that are calibrated to mantle convection simulations are often used to study the influence of mantle properties on the planet’s thermal evolution.

Parametrized thermal evolution models capture well the evolution of a mantle in vigorously convective state. This is usually appropriate for planets with a relatively thick mantle, such as Venus, Earth, Mars, and the Moon. However, the ~420 km thin mantle of Mercury is likely not vigorously convective at present, and may even be conductive. The current parameterized models do not take into account the decrease of convective visor and the Nusselt number as the mantle approaches a conductive state. This results in a poorly calibrated mantle evolution in quasi-convective state and a non-realistic discontinuity with time of heat flux at the core-mantle boundary at the cessation of convection.

We present a fully energy-conserving parametrized thermal evolution model that smoothly evolves from a convective to a conductive state. We calibrate our model to dynamical mantle convection simulations for Mercury such that it reproduces the main features of the latter.