Evolution of Convective Stresses in Stagnant-Lid Planets

Abstract

Stresses generated by convection in the mantle of rocky planets depend on the convective velocity and on the viscosity of the layer. When planets cool down, their convective motion slows down and the heat transfer becomes less efficient. The evolution of convective stresses as a function of this declining convective vigor has been described in contradictory ways, with either a decrease or an increase of stresses over time being invoked to explain some change of tectonic style when a planet cools down. In this study, 2-D Cartesian numerical simulations for a bottom-heated Newtonian fluid and scaling laws are used to show that, with a strongly temperature-dependent viscosity, convective stresses always increase, even if moderately, when the system gets colder. The stagnant-lid regime of convection for statistical steady-state is studied. The thickness of the stagnant lid and the viscous stress at its base are analyzed as a function of the temperature at the base of the model. Additional simulations with transient cooling are conducted and also exhibit an increase of convective stresses over time. The tectonic style of a planet (stagnant-lid mode or plate tectonics) is generally thought to be controlled by a fixed yield strength, with a transition from one mode to the other when the convective stresses cross this fixed limit. In this study, the evolution of convective stresses does not point to a clear temperature limit that would trigger a change of regime, and thermal evolution alone is not sufficient to explain transitions between tectonic styles.