Mantle convection models with temperature‐ and depth‐dependent thermal expansivity

Abstract

We investigate the effects of temperature‐ and depth‐dependent thermal expansivity in two‐dimensional mantle convection models in cylindrical shell and plane layer geometries. Most previous models of mantle convection have employed either a constant coefficient of thermal expansion, α, or a depth‐dependent α = α(r), where r is the radial coordinate antiparallel to gravity. We consider α to have the form α(r,T) = αr (r)αT (T), where αr(r) increases with radius, r (or decreases with depth), and αT (T) increases with temperature, T. We find that the depth dependence and temperature dependence of α each have a significant, but opposite, effect on the mean surface heat flux (or Nusselt number) and the mean surface velocity of the convecting system. For α = αr (r), a decrease of α with depth by a factor of 4 across the mantle causes a decrease of surface heat flux by about 20% and a decrease in mean surface velocity by about 30%, relative to the constant α case, in either cylindrical or plane layer geometry. However, when the temperature dependence of α is also included, αT (T) effectively compensates for the effects of αr(r) such that the predicted decreases in heat flow and surface velocity are either eliminated or, in some cases, become increases. Consequently, previous studies that include only the effects of depth dependence of α may underestimate surface heat flow and plate velocities by as much as 20% and 50%, respectively.