Thermal Runaway in the Earth's Mantle

We examine the possibility that thermal runaway may occur locally in the earth's asthenosphere, due to a coupling between the velocity and temperature fields due to a strongly temperature-dependent viscosity. The analysis is based on a partial description of convection in the earth, in which the boundary-layer nature of the motion is taken into account. We find that realistic parameter values are consistent with thermal runaway occurring on length scales of thousands of kilometers, or time scales of order 10⁸ years. If thermal runaway does occur, one would expect partial melting, and probably consequent volcanism.