Long wavelength convection, Poiseuille–Couette flow in the low-viscosity asthenosphere and the strength of plate margins

Abstract

SUMMARY Mixed heated 3-D mantle convection simulations with a low-viscosity asthenosphere reveal relatively short and long wavelength regimes with different scalings in terms of surface velocity and surface heat flux and show that mantle flow in the lithosphere–asthenosphere region is a Poiseuille–Couette flow. The Poiseuille/Couette velocity magnitude ratio, D/U, allows us to characterize solid-state flow in the asthenosphere and to predict the regime transition. The transition from dominantly pressure-driven Poiseuille flow at shorter wavelengths to dominantly shear-driven Couette flow at long wavelengths depends on the relative strength of lithosphere and asthenosphere and is associated with a switch in the dominant resistance to convective motion. In the Poiseuille regime significant resistance is provided by plate-bending, whereas in the Couette regime most resistance is due to vertical shear in the bulk mantle. The Couette case corresponds to classical scaling ideas for mantle convection whereas the Poiseuille case, with asthenospheric velocities exceeding surface velocities, is an example of a sluggish lid mode of mantle convection that has more recently been invoked for thermal history models of the Earth. Our simulations show that both modes can exist for the same level of convective vigour (i.e. Rayleigh number) but at different convective wavelengths. Additional simulations with temperature- and yield-stress dependent viscosity show consistent behaviour and suggest an association of the regime crossover with the relative strength of plate margins. Our simulations establish a connection between the strength of plate margins, solid-state flow in the asthenosphere and the wavelength of mantle convection. This connection suggests that plate tectonics in the sluggish lid mode is wavelength dependent and potentially more robust than previously envisioned.