Thermal convection heated both volumetrically and from below: Implications for predictions of planetary evolution

Solid-state thermal convection, as a model for the internal dynamics of planetary mantles, is generated both by volumetric heating and heating from below. A series of 2D and 3D numerical experiments is described where a bottom heat flux is prescribed as well as a constant fraction of volumetric heating with either free-slip or no-slip conditions for the two horizontal boundaries. The assumption that hot plumes rising in the interior of the layer act as a volumetric heat source leads to a first order scaling of thermal boundary layers. Cases with a no-slip boundary agree well with this scaling while cases with free-slip systematically deviate: a decrease of 20–30% is observed for the temperature difference across the boundary layer when the fraction of heating from below is increased from 0 to 1. These differences are attributable to a velocity structure near the boundary varying with the fraction of volumetric heating. The main planetary implications are that (i) the average thermal structure of the bulk mantle and lithosphere are not good indicators of the distribution of heat sources between the interior (e.g. radioactive heating, secular cooling) and the lower interface (e.g. core cooling); (ii) in contrast, the nature of volcanism (whether it is localized, hot spot like or widespread) reflect this distribution and should thus help to constrain the global thermal structure as well as the existence of a magnetic dynamo.