Dynamical consequences of depth-dependent thermal expansivity and viscosity on mantle circulations and thermal structure

The effects of both depth-dependent thermal expansivity and depth-dependent viscosity on mantle convection have been examined with two-dimensional finite-element simulations in aspect-ratio ten boxes. Surface Rayleigh numbers between 10⁷ and 6 × 10⁷ have been considered. The effects of depth-dependent properties, acting singly or in concert, are to produce large-scale circulations with a few major upwellings. The interior of the mantle is cooled by the many cold instabilities, which are slowed down and eventually swept about by the large-scale circulation. The interior temperature of the mantle can be influenced by the trade-off between depth-dependent properties and internal heating. For chondritic abundance of internal-heating and depth-dependent thermal expansivity, the viscosity increase across the mantle can be no greater than a factor of around ten in order to keep the lower mantle adiabatic. The thermal contrasts between the cold blobs and the surrounding mantle are strongly reduced by depth-dependent properties, whereas the lateral differences between the hot upwelling and the ambient lower mantle can be significant, over several hundred degrees. Depth-dependent properties also encourage the formation of a stronger mean-flow in the upper mantle, which may be important for promoting long-term polar motions.