High spatial resolution models of time-dependent, layered mantle convection

The degree of geochemical mixing that occurred during the mantle's early evolution is dependent on the history of convective motions in the mantle. We present time-dependent models of mantle convection that show, for certain conditions in the newly formed Earth's mantle, a transient phase of layered convection results, during which geochemical differences between the upper and lower mantle could have been preserved. The basic model assumes that the initial temperature profile for subsolidus mantle convection is strongly superadiabatic. The mantle is represented by a constant viscosity, Boussinesq fluid in a 2-D Cartesian box, heated from the bottom. The models have considerably greater spatial resolution (90 × 90 uniformly spaced grid points) than our previous work. Parameters that have been varied include the Rayleigh number (Ra = 105–108), the aspect ratio (1.4–5), the buoyancy of the initial temperature profile, and the maximum temperatures allowed for subsolidus convection. The models support our previous assertion that there is a critical value of Ra above which superadiabatic initial conditions result in a burst of convection that inverts the temperature gradient in the bulk of the mantle sufficiently to temporarily prohibit a single layer of convection; instead, two layers result. This critical value is about Ra = 106 for a mantle with the maximum amount of buoyancy; for less buoyant initial conditions, this critical value is somewhat higher. The layering lasts on the order of 109 yr for Ra = 106–108. Considering that Ra for the early mantle was certainly much larger than 106, this suggests that a transient phase of multiple layering may have prevented vigorous convection from geo-chemically homogenizing the early mantle. However, if a less buoyant initial condition prevailed, or one where supersolidus convection controls the maximum temperature of the upper mantle, the transient layering could not have taken place.