Complex Flow Structures in Strongly Chaotic Time-Dependent Mantle Convection

Abstract

Large-scale numerical simulations of two-dimensional thermal convection have been conducted in the strong time-dependent regime for infinite Prandtl number fluids, as applied to the Earth’s mantle. Both Newtonian and non-Newtonian (strain-rate proportional to the third power of the deviatoric stress) rheologies have been studied. We have also investigated for Newtonian fluids the effects of multiple phase transitions in mantle convection. The transition from soft to hard turbulence is studied for linear and nonlinear rheologies. In non-Newtonian convection with internal heating, high temperature can be produced in stagnant regions. A non-Newtonian mantle can tolerate less internal-heating than a Newtonian mantle. Non-Newtonian plumes behave quite differently from Newtonian ones in that noticeable curvatures are developed in their ascent. The transition to the disconnected-plume regime takes place at much lower Nusselt numbers for non-Newtonian rheology. For the Earth’s mantle this would have strong implications, as the upper-mantle rheology is probably non-Newtonian. At high Rayleigh number, greater than 107, convection with a single olivine to spinel phase transition becomes intermittently layered. The effects of depth-dependent thermal expansivity and internal-heating are to increase the propensity toward layering. With increasing Ra the system becomes more layered, irrespective of the sign of the Clapeyron slope and various types of phase transitions. In an early Earth with a hotter temperature and greater amounts of radiogenic heating, mantle convection would have a greater tendency for layering.