Scaling of stagnant-lid convection with Arrhenius rheology and the effects of mantle melting

Abstract

SUMMARY On the basis of numerical modelling and scaling analysis, a few modifications are proposed for the scaling of stagnant-lid convection, in order to make it more applicable to the thermal evolution of terrestrial planets. The effect of using Arrhenius rheology, as opposed to more popular linear-exponential rheology, is first investigated, and the stability analysis of top thermal boundary layer is shown to be able to capture systematic differences caused by the different kinds of temperature-dependent viscosity. The local stability analysis is then extended to handle the effects of mantle melting such as dehydration stiffening and compositional buoyancy. A new heat-flow scaling law incorporating these effects suggests that mantle melting may reduce the conventional prediction of surface heat flux by up to a factor of ∼5–10, and its potential impact on our understanding of planetary evolution is briefly discussed.