A test of approximations for modeling convection with temperature-dependent viscosity

Abstract

We compare two approximations for describing the influence of temperature-dependent viscosity on thermal convection, namely (i) depth-dependent viscosity that is controlled by the horizontally averaged temperature and (ii) viscosity that depends only on the global mean temperature. We perform two-dimensional (2-D) numerical simulations with both rigid and free slip upper boundaries and time-decaying heating from within and/or from the bottom. Monitoring the evolution of the mean temperature and surface heat flow, we find large differences between the results of approach (ii) and those of the reference model with full temperature dependence of viscosity. For approach (i) we get good agreement, especially in the stagnant-lid regime of convection. We recommend this approximation as a useful tool for modeling mantle convection and thermal evolution in planets with a stagnant lithosphere. (C) 2000 Elsevier Science B.V. All rights reserved.