On the stability of frictionally heated shear flows in the asthenosphere

Summary. Frictional heating in upper mantle shear flows may lead to localized thermal runaway and partial melting in the asthenosphere, but only as the result of a finite‐amplitude disturbance. A rigorous two‐dimensional stability analysis shows that asthenospheric shear flows are stable to small‐amplitude perturbations whether such flows are supercritical (shear stress decreases with increasing plate velocity) or subcritical (shear stress increases with increasing plate velocity). Disturbances which maintain a shear stress larger than the critical value for sufficiently long will lead to runaway. The response of the asthenosphere to events which do not satisfy this criterion must be determined by a non‐linear analysis. Reasonable models of flow in the asthenosphere could be driven to runaway, at a superexponential growth rate, by sudden increases in shear stress of less than 10 bar. Disturbances resulting from plate collisions may maintain large enough stresses for sufficiently long times to initiate runaways, while stress changes associated with large earthquakes probably occur too rapidly to do so.