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An apparent paradox is discussed, arising from the contrast between an inferred constant mantle viscosity profile and theoretical and experimental rheological flow laws, which predict a mantle viscosity function varying strongly as a function of both temperature and pressure. One can explain the paradox by a particular choice of material parameters, but then mantle temperatures (computed adiabatically) are too low; increasing the temperature by inserting compensatory thermal boundary layers is considered to be dynamically unfeasible, again because of the flow law. We consider this an impasse, and to resolve it, we suggest that old dogmas concerning boundary layers and adiabats need to be critically re-examined, to understand their basis. When this is done, we find that the observed constant viscosity is, in effect, demanded by the interplay of the rheology with the convective process, the mantle temperature is not necessarily adiabatic, and some form of layering effect may be expected, although the ideas presented here are virtually independent of the precise dynamical style of the convective motion. A consequence of these results is that explanations and extrapolations taken from constant-viscosity convection models are, a priori, unjvstifiable. (Specifically, a constant viscosity mantle is a fundamental consequence of the state of flow together with the fluid parameters and rheology: it is not a passive coincidence, which may then be used to deduce the flow state, etc.)
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