Spurious Transitions in Convective Regime Due to Viscosity Clipping: Ramifications for Modeling Planetary Secular Cooling

Abstract

AbstractThe thermal evolution of a solid planet is governed by mantle convection and therefore the dependence of viscosity on temperature. In this study, over a span of five billion years, we investigate the effect of viscosity clipping (i.e., limiting the maximum value of the viscosity) on the thermal evolution of lunar‐sized initially hot bodies featuring decaying internal heat sources. Models with a decreasing viscosity contrast resulting from limiting the maximum viscosity to 105.5 times the initial viscosity at the core‐mantle boundary were first examined. At times determined by the initial internal heating rate, rapid cooling sets in as a result of a convective regime change from stagnant‐lid to mobile‐lid convection, followed by gradual cooling to a weakly convecting and eventually nearly conductive state. Subsequently, we employ a dynamic clipping viscosity of 105.5 times the viscosity at the core‐mantle boundary, throughout the planet's evolution. In this case, stagnant‐lid convection is the only convective regime observed. Finally, convection with an initially large viscosity contrast (1010) is modeled in both 2‐D and 3‐D spherical geometry, and we find strong agreement in the thermal evolution when compared with the dynamic clipping model. Our findings show that convective regime changes due to secular cooling can occur due to implementing a fixed viscosity contrast that becomes subcritical with respect to obtaining a stagnant lid. To avoid spurious convective regime changes, the specification of a dynamic clipping viscosity can be used to emulate much higher viscosity contrasts.