Numerical investigation of a layered temperature-dependent viscosity convection in comparison to convection with a full temperature dependence

The viscosity of the Earth’s mantle is strongly variable. In particular, the dependence on temperature leads to viscosity variations of several orders of magnitude. This is crucial for the modelling of stiff surface plates in mantle convection codes but is a limiting factor in numerical experiments. Therefore, various approximations to reduce the strong vertical gradients have been applied. Here, we present an approximation that also neglects lateral variations. This layered temperature dependence has the advantage that it can easily be implemented into mantle convection codes that cannot handle lateral variations in the viscosity. Furthermore we find that typically convergence rates are improved compared to models using the full temperature dependence so that computation time can be reduced in models that would allow for the full temperature dependence. In this study we compare the results of the horizontally-averaged and the full temperature-dependent viscosity convection for a wide range of parameters comprising all three flow regimes known in thermoviscous convection and for models featuring an additional stress-dependent viscosity to allow for plate motion. Additionally, we discuss why the approximation shows minor differences to the full temperature dependence in some cases and present improvements. In general, we observe that the layered temperature-dependent viscosity convection is a suitable approximation to the full temperature depencence. Fast models of one-plate planets can be run when only using the layered temperature-dependent viscosity and plate-like motion results with an additional stress dependence.