Stagnant-lid convection: comparison of viscosity laws and uniform scaling approach for temperature and heat flux prediction

Abstract

SUMMARY Numerical simulations of stagnant-lid convection in a 2-D Cartesian fluid heated from below are carried out in order to study how the temperature dependence of the viscosity affects the vertical profile of temperature in the model. I test different viscosity laws, including the Arrhenius law with realistic parameters for the Earth’s mantle or for icy bodies. No approximation is made, which leads to extremely high viscosity contrasts. Results are compared to different approximations, in particular the Frank–Kamenetskii (FK) one. I propose a new approach for the scaling of the temperature drop across the convective part of the layer beneath the stagnant lid. The vertical profile of temperature as a function of the viscosity law is predicted, with a uniform scaling approach for all formulations of the temperature-dependent viscosity. The predicted profiles are in very good agreement with results of 2-D numerical simulations in Cartesian geometry. The complete scaling given here provides a rapid way to compare viscosity laws and to check how approximations affect the results, in terms of interior temperature, stagnant lid thickness and heat flux, compared to the real Arrhenius law for rocky mantles and for the icy outer shells of satellites. In particular, in the context of 2-D Cartesian convection heated from below, in the stagnant-lid regime, I propose a new approach to properly scale the FK formulation when it is used as an approximation of the Arrhenius law.