The influence of plate-like surface motion on upwelling dynamics in numerical mantle convection models

Abstract

Tectonic plate geometry organises the planform of convection in the Earth's mantle and is therefore expected to strongly influence mantle upwelling dynamics. We present the findings from two- and three-dimensional mantle convection simulations with plate-like surface motion and analyse how convective patterns and time-dependence change as surface plate geometry is transformed from a simple configuration permitted in 2D experiments (allowing only divergent and convergent plate boundaries) into arrangements requiring three-dimensional modelling. Our experiments model vigorous convection ( Ra = 10 7 based on the upper mantle viscosity) in a stratified viscosity system featuring both internal and basal heating. We first consider a suite of two-dimensional experiments and determine an estimate for a uniform surface velocity that is comparable in magnitude to the mean transit time for the upwellings associated with the system. We argue that a surface velocity that neither forces nor resists the convectively driven flow meets this requirement but show that temporally varying and constant plate velocities can both satisfy this condition over a given period of time with different results. For the partially internally heated, aspect ratio 4 cases considered here, we choose a fixed velocity boundary condition and find this velocity is about 23% lower than the mean velocity obtained with a free-slip surface condition in an otherwise identical model. The plate velocity obtained from our two-dimensional experiments is then adopted for our three-dimensional calculations that include plates as plate geometry is systematically varied. For the parameters specified in our study (which result in a basal heat flux of approximately 50% the surface value and a viscosity contrast of a factor of 30 between the upper and lower mantle) steady plume-like upwellings are present in both free-slip and rigid surface calculations. However, a surface boundary condition featuring a pair of congruent plates moving in opposing directions with a velocity comparable to the plume transit time forces the convective planform into a roll-like pattern featuring essentially sheet-like upwellings positioned below the divergent plate boundary. When plate geometries are specified in a way that produces offset segments of convergent and divergent boundary joined by boundaries characterised by strike-slip motion, the planform of the underlying convection organises into patterns featuring columnar, plume-like, upwellings. Using calculations of upwelling advective heat flux to determine plume locations, we track plume motion in the upper and lower mantle over periods of several plume rise times. We show that long-lived, nearly stationary, plumes appear in calculations featuring surface velocities comparable to the mean vertical velocity of the upwellings and that the associated plume heads remain positioned below intraplate positions for periods that can exceed tens of millions of years.