The viscosity of planetary mantle material is strongly temperature dependent. This dependence is described by an Arrhenius law. But for the realistic viscosity contrast that appears over the depth of the mantle, strong gradients in the upper thermal boundary layer occur. These strong gradients are not realizable in numerical models. Therefore, the Frank-Kamenetskii approximation, leading to a linearized exponential viscosity function, is commonly used. Much research on the plate-mantle system has been done applying the Frank-Kamenetskii rheology. The question though still arises, if these results can be reproduced when using the Arrhenius law. Here it has to be kept in mind, that in numerical models the realistic viscosity contrast appearing over the mantle can neither be coped with by the Arrhenius nor the Frank-Kamenetskii approach. Thus, the computational aspects to date only allow for viscosity contrasts being moderate as compared to realistic values and extrapolations to planet-like values have to be made for both rheologies. Comparing results obtained by the commonly used forms of the Arrhenius and the Frank-Kamenetskii approach, we observe the same change in flow behavior from mobile-lid to stagnant-lid convection. The differences are only of quantitative nature: In the stagnant-lid regime, some Arrhenius formulations lead to a thinner top boundary layer which results in values of lithospheric thicknesses being more realistic. Here it has to be noted that different forms of the Arrhenius law have been used which differ among themselves. When properly scaled, the differences between the Frank-Kamenetskii and Arrhenius rheology can, however, be strongly diminished. To understand general features in the plate tectonics-mantle convection system an additional stress dependence of the viscosity has to be considered. The discrepancies between the various viscosity formulations are then of even less importance, because for an Earth-like convection regime, the top viscosity is more strongly influenced by the stress dependence rather than by the temperature dependence.
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