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.
Bibliographical noteFunding Information:
This research has been supported by NASA, NSF, Deutsche Forschung Gemeinschaft, the Von Humboldt Stiftung, the American—German Fu!-bright Program, and the Danish Research Academy. We thank R. Boehler A. Chopelas and v. Steinbach for discussions. M. Lundgren, T. Bui and J. Smedsmo helped in the preparation of the manuscript.