A sensitivity study of three‐dimensional spherical mantle convection at 10⁸ Rayleigh number: Effects of depth‐dependent viscosity, heating mode, and an endothermic phase change

Abstract

Mantle convection is influenced simultaneously by a number of physical effects: brittle failure in the surface plates, strongly variable viscosity, mineral phase changes, and both internal heating (radioactivity) and bottom heating from the core. Here we present a systematic study of three potentially important effects: depth‐dependent viscosity, an endothermic phase change, and bottom versus internal heating. We model three‐dimensional spherical convection at Rayleigh Ra =10 8 thus approaching the dynamical regime of the mantle. An isoviscous, internally heated reference model displays point‐like downwellings from the cold upper boundary layer, a blue spectrum of thermal heterogeneity, and small but rapid time variations in flow diagnostics. A modest factor 30 increase in lower mantle viscosity results in a planform dominated by long, linear downwellings, a red spectrum, and great temporal stability. Bottom heating has the predictable effect of adding a thermal boundary layer at the base of the mantle. We use a Clapeyron slope of γ=−4 MPa °K −1 for the 670 km phase transition, resulting in a phase buoyancy parameter of P =−0.112. This phase change causes upwellings and downwellings to pause in the transition zone but has little influence on the inherent time dependence of flow and only a modest reddening effect on the heterogeneity spectrum. Larger values of P result in stronger effects, but our choice of P is likely already too large to be representative of the mantle transition zone. Combinations of all three effects are remarkably predictable in terms of the single‐effect models, and the effect of depth‐dependent viscosity is found to be dominant.