Viscous forces acting on subducting lithosphere

Abstract

Subducting lithosphere is driven by gravitational forces and resisted primarily by viscous forces. Three independent types of mantle flow combine to create viscous tractions on the surface of a subducting slab which terminates in the upper mantle: (1) flow induced by plate convergence and slab subduction, (2) flow caused by trench migration, and (3) “regional” upper mantle flow unrelated to convergence or trench migration. The equilibrium dip of a slab reflects a balance of viscous tractions with gravitational forces and slab stiffness. We present results from a two‐dimensional finite difference model of upper mantle flow for different slab geometries where mantle viscosity increases exponentially with depth and the slab, terminating in the upper mantle, is assumed to be infinitely viscous. In the overlying mantle wedge the subducting slab creates a strong eddy, which is largely unaffected by trench migration or regional flow. Trench migration and regional mantle flow produce tractions which tend to lift the slab and which are independent of slab dip for a slab terminating in the upper mantle. For dips >22.5° the upward torquing force on the slab due to convergence is negligible compared to the pressures created by trench migration and regional mantle flow. Slabs dipping <87.5° which are in torquing equilibrium require regional flow in the same direction as subduction (or trench migration in the opposite direction), which simultaneously tends to eliminate most of the horizontal pressure difference across the subduction zone. The force calculations based on this model suggest that viscosity at the base of the lithosphere is <2×1020 Pa s, assuming viscosity increases exponentially with depth to <2.8×1021 Pa s just above the lower mantle. For force‐balanced slabs which penetrate halfway into the upper mantle with dip in the range of 30° to 75° slab dip increases linearly with decreasing trench migration rate and decreasing regional mantle flow.