Convection with pressure- and temperature-dependent non-Newtonian rheology

Abstract

The influence of non-linear stress-strain rate relation on thermal convection in a fluid whose rheological properties are also pressure- and temperature-dependent is studied in a series of numerical models. A finite element method with an upwind weighted residual technique and B splines is applied to obtain steady state and time-dependent solutions of two-dimensional convection in rectangular enclosures. A cubic power law rheology is taken in most cases and the result is compared to Newtonian convection. The model calculations comprise different effective Rayleigh numbers in the range of 104-106, different values for the activation energy and volume which determine the p, T dependence, different modes of heating, different aspect ratios, and different mechanical boundary conditions. In almost all cases power-law rheology leads to considerably different flow patterns and heat transfer properties than those predicted for Newtonian convection. In general the effect is to reduce the internal viscosity contrast which is produced by the pressure and temperature effect. This can in some cases mobilize regions of the cell which are stagnant in the case of Newtonian rheology. The properties of stationary power-law convection can be imitated closely by Newtonian flow with a reduced value for the activation enthalpy βH⋆ with β=0.3-0.5. If the stress exponent is greater than 3, the p, T influence is reduced even more. In the time-dependent regime non-linear rheology enhances oscillatory behaviour, increasing the amplitude and leading to peak-line maxima and broad minima. The question of proper evaluation of the average viscosity or effective Rayleigh number in variable viscosity convection is also addressed. Empirically it was found to be more satisfactory to weight the local viscosity with the absolute value of the strain rate rather than with its square as was proposed earlier. Further points under consideration were the effects of combined linear and non-linear rheology and the parametrization of variable viscosity convection. It appears possible that non-Newtonian convection plays a key role in determining the convective style in a planetary mantle. Non-Newtonian convection might be essential for facilitating flow in the Earth's lower mantle, for making the upper thermal boundary layer behave like a quasi-rigid but subductable plate, or for stabilizing a hot low-viscosity boundary layer.