Dynamical effects of a temperature- and pressure-dependent lower-mantle rheology on the interaction of upwellings with the transition zone

Volker Steinbach, David A. Yuen

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We have examined the consequences of a temperature- and pressure-dependent lower-mantle viscosity on the interaction of upwellings with the two major phase transitions. The viscosity used is only temperature-dependent in the upper-mantle but assumes both temperature- and pressure dependences in the lower-mantle. The activation enthalpy increases with depth dependence scaled after experimental melting curves of lower-mantle components. We have employed a two-dimensional cartesian box with an aspect-ratio of five and a mantle layer thickness of 2900 km, using an extended Boussinesq model with a depth-dependent thermal expansivity. Latent heat release and viscous dissipation have been included in the temperature equation. We have considered models both without and with a viscosity jump (a factor of 8) across the 660 km boundary. The range of averaged Rayleigh numbers (Ra) considered lies between 2 × 106 and 107. A major effect of this temperature-and pressure-dependent rheology is the stabilization of the upwelling plumes and the increase of viscous heating in the bottom portion of these plumes. The impingement of these heated plumes at the endothermic phase boundary causes the development of secondary plumes to rise into the upper-mantle. Shear-heating together with the latent heat release produces large temperature increases in the plumes passing through the transition zone, which may cause melting in the deep upper-mantle. Although the average Rayleigh number in the case of temperature- and pressure-dependent viscosity is around a factor of 5 lower than in a case with purely temperature-dependent viscosity, the resulting flow is only slightly less layered, which is contrary to the earlier finding of Christensen and Yuen (1985). The tendencies for the development of secondary plumes and high temperatures inside the upwellings are enhanced by the viscosity jump at the 660 km boundary. In this situation few nearly steady, vigorous upwellings exist in the lower mantle, while in the upper mantle vigorous time-dependent convection takes place. For an averaged Rayleigh number of 107, the system becomes layered with many thin plumes appearing in the lower mantle.

Original languageEnglish (US)
Pages (from-to)85-100
Number of pages16
JournalPhysics of the Earth and Planetary Interiors
Issue number1-2
StatePublished - Oct 1997

Bibliographical note

Funding Information:
We acknowledge stimulating discussions with S. Zhang, T. Nakakuki, and B.S. Schroeder. V.S. was a recipient of a Minnesota Supercomputer traveling grant. This research has been supported by the German DFG and the US National Science Foundation (Ocean Sciences Program). Computations have been carried out through the University of Minnesota-IBM Shared Research Project and the Computing Center of Cologne University.


  • Lower mantle viscosity
  • Mantle upwellings
  • Rayleigh numbers
  • Temperature and pressure-dependent rheology
  • Upwelling plumes


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