Extended-Boussinesq thermal–chemical convection with moving heat sources and variable viscosity

We have studied with an aspect-ratio four box the thermal–chemical convective evolution with strongly temperature- and depth-dependent viscosity and moving heat sources within the extended-Boussinesq framework, in which both adiabatic and viscous heating are included and a depth-dependent thermal expansivity is assumed in the equation of state. Our focus is to show how this type of mantle evolution with an averaged Ra of 0(106) may develop with a linear chemical stratification and a uniformly hot mantle as an initial condition. The effects of extended-Boussinesq and depth-dependent thermal expansivity are to prevent the effective destruction of the chemical heterogeneities. Our results show that this initial condition would, after the age of the Earth, lead to a ‘lava lamp’ mode consisting of a thick chemically stratified and intensely internally heated layer with a thickness of around a quarter of the whole mantle thickness. However, in this isolated internally convecting layer, exceedingly high temperatures greater than 4500 K would be reached in the deep mantle. Plumes can be launched from the top of this thick denser layer. This ‘lava lamp’ stage would give way to the formation of denser hill-like structures at the core–mantle boundary. Then upwellings with deep lower mantle origins can be induced by the interaction of the downwellings with the D″ layer. Our simulations show the possibility for some long-range mass transfer interaction between these widely separated chemical hills promoted by the fast horizontal flow induced by the sinking currents along the low-viscosity zone due to temperature-dependent rheology at the core–mantle boundary.