A simple model of plate generation from mantle flow

SUMMARY A simple model of non‐Newtonian creeping flow is used to evaluate classes of rheologies which allow viscous mantle flow to become plate like. The model describes shallow‐layer lithospheric motion driven by sources and sinks. The sources represent spreading ridges, while the sinks represent subduction zones; the sources and sinks thus also prescribe the poloidal component of the surface flow field. The toroidal (strike‐slip) component of the flow field is found via the solution of the Stokes equation with non‐Newtonian rheology. As a first basic investigation of the model, the horizontal divergence from the 2‐D rectangular velocity field of Olson & Bercovici (1991) is used for the source‐sink field. The degree to which the induced fluid flow reproduces the rectangular plate is used to measure the success of different rheologies in generating plate‐like flows. Results indicate that power‐law rheologies, even in the limit of very high power‐law index v , can only produce modest plate‐like flow. For example, the ratio of toroidal‐to‐poloidal kinetic energy for a source‐sink field derived from a square plate is at best 0.65, whereas a perfect square plate has a ratio of 1.0. Moreover, the power‐law rheology appears to reach an asymptotic limit in its ability to produce plate‐like behaviour. This implies that plate tectonics is unlikely to arise from a power‐law rheology even in the limit of very high Y. A class of rheologies that yield significantly more promising results arise from the Carreau pseudo‐plastic rheology with the power‐law index taken to be v < 0. One rheology in this class is the continuum model for stick‐slip, Earthsuake behaviour of Whitehead & Gans (1974), which is essentially the Carreau equation with v = ‐1. This class of rheologies, referred to as the stick‐slip rheologies, induces a toroidal‐to‐poloidal kinetic‐energy ratio for the source‐sink function of a square plate which can be as high as 0.9. The viscosity (or strength) distribution for this class of rheologies also appears more plate like, showing fairly uniform high‐viscosity regions (pseudo‐plates) and sharply defined low‐viscosity zones (pseudomargins). In contrast, even the most non‐linear power‐law rheology produces spatially varying high‐viscosity regions and relatively smooth low‐viscosity margins. The greater success of the stick‐slip rheologies in producing plates is attributed to a self‐lubricating mechanism in which the transfer of momentum from regions of high shear to low shear is inhibited. In contrast, even in the limit of infinite power‐law index, a power‐law rheology can retard but never prohibit momentum transfer. This feature is essential to the sharpening of velocity profiles into plate‐like profiles, which is illustrated with a simple boundary‐layer theory.