Dynamics of free subduction from 3-D boundary element modeling

In order better to understand the physical mechanisms underlying free subduction, we perform three-dimensional boundary-element numerical simulations of a dense fluid sheet with thickness h and viscosity eta(2) sinking in an 'ambient mantle' with viscosity eta(1). The mantle layer is bounded above by a traction-free surface, and is either (1) infinitely deep or (2) underlain by a rigid boundary at a finite depth H + d, similar to the typical geometry used in laboratory experiments. Instantaneous solutions in configuration (1) show that the sheet's dimensionless 'stiffness' S determines whether the slab's sinking speed is controlled by the viscosity of the ambient mantle (S < 1) or the viscosity of the sheet itself (S > 10). Time-dependent solutions with tracers in configuration (2) demonstrate a partial return flow around the leading edge of a retreating slab and return flow around its sides. The extra 'edge drag' exerted by the flow around the sides causes transverse deformation of the slab, and makes the sinking speed of a 3-D slab up to 40% less than that of a 2-D slab. A systematic investigation of the slab's interaction with the bottom boundary as a function of eta(2)/eta(1) and H/h delineates a rich regime diagram of different subduction modes (trench retreating, slab folding, trench advancing) and reveals a new 'advancing-folding' mode in which slab folding is preceded by advancing trench motion. The solutions demonstrate that mode selection is controlled by the dip of the leading edge of the slab at the time when it first encounters the bottom boundary.