Some geodynamical effects of anisotropic viscosity

Abstract

Rheological anisotropy in the mantle may arise from various causes, the most important are the preferred orientation of single crystals, and the orientation of streaks of eclogitic material in a ‘marble cake’ mantle. In both cases the orientation can be achieved by the flow kinematics, and in steady state convection the planes of easy slip will eventually be orientated parallel to the stream lines. The dynamic equations for a 2-D, incompressible, anisotropic viscous fluid are derived, and some geodynamic consequences are studied. A difference of the order 10–100 between ‘shear’ and ‘normal’ viscosity is considered. Post-glacial rebound would be affected by the mechanical properties in deeper parts of the mantle. The observed uplift history near the ice margin has been taken as argument against strong viscosity stratification in the mantle. It is shown here that with strong viscous anisotropy at least in the upper mantle, the uplift history is compatible with a significant increase in viscosity between upper and lower mantle. The topographic and geoid signal can show a spatial offset from a generating mass anomaly in the mantle. This may provide the opportunity for in situ observation of anisotropic flow properties in the mantle. In numerical case studies of steady state convection streamline-orientated anisotropy is considered. At high Rayleigh number for bottom-heated convection the formation of velocity boundary layers is observed, with no flow in the stagnant core of the convection cell. With internal heating or strong pressure- and temperature-dependence of viscosity this is no longer found, but in the latter case anisotropy enhances the channelling of flow into low-viscosity regions, e.g. hot rising plumes. A few experiments have been performed for time-dependent convection. The results suggest that the onset of time-dependent boundary layer instabilities may be somewhat retarded, but would not be strongly suppressed by anisotropy. Strong time-dependence may destroy any large-scale coherence in the orientation of anisotropy and thus render the mantle to appear viscously isotropic.