Comparing the Dynamics of Free Subduction in Cartesian and Spherical Domains

The effects of sphericity are regularly neglected in numerical and laboratory studies that examine the factors controlling subduction dynamics. Most existing studies have been executed in a Cartesian domain, with the small number of simulations undertaken in a spherical shell incorporating plates with an oversimplified rheology, limiting their applicability. Here, we simulate free-subduction of composite visco-plastic plates in 3-D Cartesian and spherical shell domains, to examine the role of sphericity in dictating the dynamics of subduction, and highlight the limitations of Cartesian models. We identify two irreconcilable differences between Cartesian and spherical models, which limit the suitability of Cartesian-based studies: (a) the presence of sidewall boundaries in Cartesian models, which modify the flow regime; and (b) the reduction of space with depth in spherical shells, alongside the radial gravity direction, which cannot be captured in Cartesian domains. Although Cartesian models generally predict comparable subduction regimes and slab morphologies to their spherical counterparts, there are significant quantitative discrepancies. We find that simulations in Cartesian domains that exceed Earth's dimensions overestimate trench retreat. Conversely, due to boundary effects, simulations in smaller Cartesian domains overestimate the variation of trench curvature driven by plate width. Importantly, spherical models consistently predict higher sinking velocities and a reduction in slab width with depth, particularly for wider subduction systems, enhancing along-strike slab buckling and trench curvature. Results imply that sphericity must be considered for understanding the dynamics of Earth's wider subduction systems, and is already a significant factor for slabs of width 2,400 km. Plain Language Summary Subduction zones delineate tectonic plate boundaries where one plate descends beneath another into the underlying mantle. Subduction is responsible for many of Earth's most distinctive geological features, including mountain belts, volcanic island arcs, and deep sea trenches. It has long been recognized that the shape of subduction zones is influenced by Earth's sphericity, but sphericity's importance for other aspects of subduction dynamics remains unclear, as the majority of existing modeling studies have been carried out in (easier to simulate) rectangular computational domains. Here, using subduction models with viscosity laws appropriate to mimic plate-like behavior, we compare predictions from rectangular and spherical models. We show that because rectangular models cannot capture the reduction in space with increasing depth, they consistently underestimate sinking velocities of the subducting plate, which determine how plate temperatures and strength evolve during sinking. Furthermore, the difference in flow patterns that develop in rectangular and spherical models changes how the subducting plates bend, buckle and migrate. Our models show that the discrepancy between Cartesian and spherical subduction models increases with plate width. Results imply a critical width of less than 2,400 km at which sphericity must be considered when simulating Earth's subduction systems.