The effects of a composite non‐Newtonian and Newtonian rheology on mantle convection

A finite element method based on a primitive variables formulation is used to model both steady‐state and time‐dependent mantle convection with a composite Newtonian and non‐Newtonian (power‐law) rheology. The rheological model employs the transition stress as a means of partitioning the relative importance of the two rheologies. Results show that there is no direct correlation between viscosity and temperature anomalies. Fluctuations of the velocity fields are much greater and faster than for Newtonian flows. Fluctuations with amplitudes several times the background velocity are quite common. Intermittency effects with quiescent periods punctuated by chaotic bursts are observed. From scaling arguments temporal fluctuations of the volume‐averaged viscosity are comparable in magnitude to the variations in the surface heat flow for the non‐Newtonian flows, but are smaller than the variations in the velocity field. At larger transition stress the Newtonian behaviour becomes dominant and the temporal variations of the viscosity diminish. Both steady‐state and time‐dependent results show that for a given transition stress the non‐Newtonian behaviour prevails to a greater extent with increasing Rayleigh number. Implications of this non‐Newtonian tendency for Archaean tectonics are discussed.