Two-dimensional numerical experiments on mantle convection with stress-history-dependent rheology: toward self-consistent reproduction of plate tectonics

Abstract We developed a numerical model of thermal convection of highly viscous incompressible fluids, aiming at reproducing plate tectonics in the framework of mantle convection. A two-dimensional basally-heated convection is considered under the Boussinesq approximation in a half of cylindrical annulus whose inner and outer radii are close to those of the Earth’s mantle. The viscosity is assumed to nonlinearly depend on “degree of damage” as well as temperature and pressure. The heart of the present rheology model lies in the hysteresis between the “intact” and “damaged” branches at low and high stress, respectively. The hysteresis induces the dependence on stress-history in viscosity for a particular range of applied stress, which enables us to distinguish the stiff plate interiors and weak plate boundaries. In a series of calculations by systematically varying the temperature-dependence in viscosity, we obtained a regime of convection where the nature of highly viscous cold fluid is quite similar to that of the Earth’s plates at an intermediate temperature-dependence; the layer of cold viscous fluid is divided into several pieces of rigid plates each of which horizontally moves, and the surface heat flow decreases with the distance from the divergent margin (ridge) in accordance with the half-space cooling. A careful analysis on the mechanical states in the cold thermal boundary layer (cTBL) showed that the occurrence of the “plate-like” (PL) convection is closely related to the hysteresis in viscosity; the PL convection takes place only when the stress level $$\sigma _\text {cTBL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mtext>cTBL</mml:mtext> </mml:msub> </mml:math> in cTBL, estimated from the ridge-push force, can induce the stress-history dependence in viscosity. By comparing the convecting flow structures in our experiments with the earlier ones Using 2-D Cartesian geometry, we also found that $$\sigma _\text {cTBL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mtext>cTBL</mml:mtext> </mml:msub> </mml:math> is almost unchanged for both cases, which results in the occurrence of the PL mode under very similar conditions regardless of the model geometries. Our findings not only highlight the ultimate importance of stress-history-dependent rheology in the self-consistent reproduction of tectonics plates, but also offer hints for future attempts toward integrated models of mantle convection and plate tectonics in three-dimensional spherical geometry. Graphical Abstract