Time‐dependence in mantle convection models featuring dynamically evolving plates

SUMMARY We present the findings from a study of 2‐D Cartesian geometry mantle convection simulations carried out to determine how plate velocities and the surface and basal heat flux respond to an evolving plate geometry. We model flow for periods equating to hundreds of millions of years and find that while calculations that feature fixed plate geometries exhibit regular reversals in plate motion, this behaviour is absent in models featuring evolving plate boundaries. However, simulations featuring evolving plate boundaries and plates with either a fixed‐thickness or temporally varying thickness are highly time‐dependent and their globally averaged mean plate velocities are higher than in simulations featuring static plate geometries. Our models featuring evolving plate geometries assume that (1) young plates override old plates with the velocity of the younger plate and (2) that symmetric seafloor spreading occurs at divergent plate boundaries. Plate velocities are dynamically determined in accord with a force‐balance modelling approach and the plate velocities determine the dynamic evolution of the plate boundaries according to criteria (1) and (2), above. Plates in our calculations are highly viscous and are treated as rigid blocks for the purpose of determining whether they will break according to a yield stress criterion. The modelling of plate rifting means that both the number and mean size of the plates in our calculations are time‐dependent. We focus on isolating the influence of plate thickness on time‐dependent flows and examine the time‐dependence of global plate velocities and mantle and core heat flow. In an initial study of unit aspect ratio models we find that there is a transition in the character of time‐dependent behaviour as the model plate thickness is increased. Plates that are comparable in thickness to the mean thickness of the thermal boundary layer exhibit periodic reversals. Plates that are much thinner than the thermal boundary layer exhibit no reversals. Intermediate thickness plates reverse intermittently. In aspect ratio 12 calculations, we find that the mean global plate velocity can exhibit variations of more than a factor of two over periods of tens of millions of years. We also find that the mean surface velocity of the plates and the mean global heat flux rise and fall in tandem (although high frequency variations in the global velocity are not reflected in the heat flux time‐series). In a simulation spanning almost 3 Gyr we observe several instances of surface heat flux fluctuations of 40–50 per cent occurring within periods of 75–200 Myr.