Fluid mechanical representation of plate boundaries in mantle convection modeling

We present a self-consistent two-dimensional model of mantle convection with plate-like motion in the highly viscous surface layer driven only by the excess mass of subducted slabs. Trenches and ridges are represented by conjugate pairs of 45°45°-dipping reverse and normal faults, respectively. The negative buoyancy effect of highly viscous subducting slab is represented by sheet-like mass anomalies at the bottom of the surface layer. All the expressions are obtained in analytic forms. We treat flow driven by slab excess mass, faulting at trenches and faulting at ridges as separate systems with common boundary conditions. A given mass-driven convection system is linearly coupled with the other two systems by the frictionless nature of the fault planes at trenches and by the zero-tensile strength nature of the fault system at ridges. In this coupled system with a large viscosity contrast between the surface and underlying layers, flow velocity is practically uniform throughout the surface layer and changes its direction only across the fault planes. A unique feature of this system is the surface flow velocity that depends little on lithosphere viscosity but is primarily controlled by asthenosphere viscosity. The surface flow velocity only weakly depends on ridge–trench distance. The values of flow velocity and stresses in the surface layer with a reasonable range of asthenosphere viscosity are in broad agreement with observations of plate motion.