A simple model of plate generation from mantle flow

Abstract

SUMMARY A simple model of non-Newtoniancreepingflow is used to evaluate classes of rheologieswhichallow viscous mantle flow to becomeplate-like. The model describes shallow-layerlithosphericmotion driven by sources and sinks. The sources represent spreading ridges while the sinks rep-resent subduction zones; the sources and sinks thus also prescribe the poloidal component ofthe surface flow field. The toroidal (strike-slip) component of the flow field is found via thesolution of the Stokes equation with non-Newtonian rheology. As a first basic investigation ofthe model, the horizontal divergence from the two-dimensional rectangular velocity field ofOlson & Bercovici (1991) is used for the source-sink field. The degree to which the inducedfluid flow reproducesthe rectangularplate is used to measure the success of differentrheologiesin generating plate-like flows. Results indicate that power-law rheologies, even in the limit ofvery high power-law indexν, can only produce modest plate-like flow. For example, the ratioof toroidal to poloidal kinetic energy for a source-sink field derived from a square plate is atbest 0.65, whereas a perfect square plate has a ratio of 1.0. Moreover, the power-law rheologyappears to reach an asymptotic limit in its ability to produce plate-like behavior. This impliesthat plate tectonics is unlikely to arise from a power-law rheology even in the limit of very highν. A class of rheologies that yield significantly more promisi ng results arise from the Carreaupseudo-plastic rheology with the power-law index taken to be ν < 0. One rheology in thisclass is the continuum model for stick-slip, earthquake behavior of Whitehead & Gans (1974),which is essentially the Carreau equation with ν = −1. This class of rheologies, referred to asthe stick-slip rheologies, induces a toroidal to poloidal kinetic energy ratio for a square plates’ssource-sink function which can be as high as0.9. The viscosity (or strength) distribution forthis class of rheologies also appears more plate-like, showing fairly uniform high viscosity re-gions (pseudo-plates) and sharply defined low viscosity zones (pseudo-margins). In contrast,even the most nonlinear power-law rheology produces spatially varying high viscosity regionsand relatively smooth low viscosity margins. The greater success of the stick-slip rheologiesin producing plates is attributed to a self-lubricating mechanism in which the transfer of mo-mentum from regions of high shear to low shear is inhibited. In contrast, even in the limit ofinfinite power-law index, a power-law rheology can retard but never prohibit momentum trans-fer. This feature is essential to the sharpening of velocity profiles into plate-like profiles, whichis illustrated with a simple boundary-layertheory.Key words: Plate tectonics, mantle convection, non-Newtonian flow, toroidal-poloidal cou-pling.