Thermal convection in a volumetrically heated, infinite Prandtl number fluid with strongly temperature-dependent viscosity: Implications for planetary thermal evolution

Parameterized models of the thermal evolution of planets are usually based on the assumption that the lithosphere-convecting mantle boundary can be defined by an. isotherm at a temperature below which viscosity is infinite on geologic timescales. Recent experimental results argue against this assumption. We have investigated both the definition of the lithosphere-convecting mantle boundary and the power law relation describing convecting heat transfer, based on numerical experiments of thermal convection in a volumetrically heated fluid with temperature-dependent viscosity. Other recent studies have treated only the heating from below, but volumetric heating is likely to be the dominant mode of heating in planetary mantles, either as a consequence of radioactive heating or as a proxy for secular cooling. Convection can occur either in the whole box or be located under a stagnant lid. In the lid regime, convection is driven by a temperature contrast depending on the rheology of the fluid and the interior temperature. This result, in agreement with experimental studies, indicates' that boundary between the stagnant lid and the convecting layer (similar to the lithosphere-convecting mantle boundary) cannot be defined as a fixed isotherm. During thermal evolution of planets, the viscosity contrast in the convecting mantle remains constant, not the temperature at the bottom of the lithosphere. We present an example showing that the evolution of planets is strongly dependent on the criterion chosen to define the lithosphere-convecting mantle boundary. For reasonable values of the activation energy for thermally activated creep, the temperature defining the lithosphere-convecting mantle boundary, the mantle temperature, and the thickness of the lithosphere could be larger than expected from previous models which treat the base of the lithosphere as a fixed isotherm.