Asthenospheric shear flow: Thermally stable or unstable?

One‐dimensional shear flows may decouple certain lithospheric plates from the deeper mantle, especially beneath continental shields. We investigate the variety of such flows which can occur in a model upper mantle with an olivine rheology and radiogenic heat sources. The thermal stability of these states is examined. The flows are stable if the horizontal velocity at the top of the mantle is fixed. If, on the other hand, the shear stress is fixed, instability may occur due to viscous heating associated with the strong temperature dependence of the olivine rheology. The boundary condition relevant to the real earth is undoubtedly neither of these.