Institut für Geophysik Geschäftsführender Direktor:
Prof. Dr. Ulrich Hansen

Corrensstraße 24 48149 Münster
Tel.: +49 251 83-33590
Fax: +49 251 83-36100

A new method to simulate convection with strongly temperature- and pressure-dependent voscosity in a spherical shell: Applications to the Earth's mantle

Kai Stemmer, Helmut Harder, Ulrich Hansen


We present a new finite volume code for modeling three-dimensional thermal convection in a spherical shell with strong temperature- and pressure-dependent viscosity. A new discretization formulation of the viscous term, tailored to the finite volume method on a colocated grid, enables laterally variable viscosity. A smoothed cubed–sphere grid is used to avoid pole problems which occur in latitude–longitude grids with spherical coordinates. The spherical shell is topologically divided into six cubes. The equations are formulated in primitive variables, and are treated in the Cartesian cubes. In order to ensure mass conservation a SIMPLER pressure correction procedure is applied and to handle strong viscosity variations of Δη = 107 and high Rayleigh numbers of Ra = 108 the pressure correction algorithm is combined with a pressure weighted interpolation method to satisfy the incompressibility condition and to avoid oscillatory pressure solutions. The model is validated by a comparison of diagnostical parameters of steady-state cubic and tetrahedral convection with other published spherical models and a detailed convergence test on successively refined grids. Lateral variable fluid properties have a significant influence on the convection pattern and heat flow dynamics. The influence of temperature- and pressure-dependent viscosity on the flow is systematically analyzed for basal and mixed-mode heated thermal convection in the spherical shell. A new method to classify the simulations to the mobile, transitional or stagnant-lid regime is given by means of a comparison of selected diagnostical parameters, a significantly improved classification as compared to the common surface layer mobility criterion. A scaling law for the interior temperature and viscosity in the stagnant-lid regime is given. Purely basal heating and strongly temperature-dependent rheology stabilize plume positions and yield with a weak time dependence of the convecting system, while the amount of additional internal heating controls the strength of time dependence. Strength and partitioning of basal and internal heat sources in the mantle seems to be of major importance to specify the dynamics of the flow field and therefore the evolution of the Earth and other planets. Additional pressure dependence strongly influences the dynamics even if the magnitude of pressure variation is relatively small. For an appropriate combination of pressure and temperature dependence we observe a kind of low and high viscosity zone in the asthenosphere and deep in the mantle. The viscosity–depth profile of such a flow shows striking similarities to viscosity profiles from inversion of seismic, geoid and post-glacial rebound data.


  Physics of the earth and Planetary Interiors, 157(2006), 223 - 249


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Institut für Geophysik Geschäftsführender Direktor:
Prof. Dr. Ulrich Hansen

Corrensstraße 24
· 48149 Münster
Tel.: +49 251 83-33590 · Fax: +49 251 83-36100
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