Numerical evaluation of mantle plume spacing, size, flow rates and unsteadiness

Abstract

Predictions of several characteristics of mantle plumes from boundary layer theory have been tested and calibrated with numerical models in cylindrical coordinates. Instability spacing in the initial stages of the numerical models is well predicted as are the lift-off time of plume heads, the size of plume heads at lift-off, and the heat flow of individual plume tails. However, since the prediction quality for the instability spacing and the lift-off time of plume heads deteriorates in the presence of larger heterogeneities in the thermal boundary layer, these predictions seem not very useful for mantle plumes. Predictions for the plume head size at lift-off appear to be largely independent of the degree of boundary layer heterogeneity and therefore may provide reasonable estimates for mantle plumes. The predictions for the heat flow of a plume tail seem to yield usable results for both stationary plume tails and those that show at least periods of quasi-stationary heat flow. Assuming that mantle plumes are reasonably steady, the prediction formula is used to derive estimates for the temperature difference ΔTl across the thermal boundary layer at the core-mantle boundary. This depends on the fraction of the core surface that is presumed to be occupied by plume feeding areas. Taking this fraction to be greater than 1/2 yields ΔTl < 400°C, too low to be compatible with petrological constraints on plumes. Smaller fractions yield larger ΔTl, but this seems to be incompatible with the geophysical distribution of hotspots.