Structure of axisymmetric mantle plumes

Abstract

Results of high‐resolution numerical calculations of axisymmetric thermal plumes in an infinite Prandtl number fluid with thermally activated viscosity are used to infer the structure of axisymmetric subsolidus thermal plumes in the Earth's lower mantle. We calculate the velocity and temperature distribution for axisymmetric convection above a heated disk in an incompressible fluid cylinder, 2400 km in height and 1200 km in diameter, initially at a uniform temperature T∞. The lower boundary, representing the plume source region near the core‐mantle boundary, is stress‐free and maintained at temperature Tc> T∞. The upper boundary is permeable, allowing the plume to escape the cylinder. We determine the sensitivity of plume structure to viscosity variations η∞/ηc ranging from 102 to more than 104 and temperature differences ΔT = Tc ‐ T∞. in the range 400–850 K. Starting plumes consist of a large leading diapir and a trailing conduit connected to the thermal boundary layer above the heated surface. The leading diapir expands during ascent, to about 400 km diameter at 2200 km height. In steady state, the plume consists of a narrow, high‐velocity conduit imbedded within a broader thermal halo. The width of both these structures is proportional to height above the heated boundary and inversely proportional to ΔT and the viscosity ratio. Heat transport in the plume is nearly independent of viscosity variations. A simplified boundary layer model yields a heat transfer law, Nu ≈ Ra⅓ where Nu is the plume Nusselt number and Ra is the Rayleigh number based on, ΔT, η∞ and the radius of the heated circular region feeding the plume. Calculated steady state plume heat transports fit this law to within a few percent. We present several calculations of plumes with heat transport in the range 100–400 GW, similar to the advective heat transport by the Hawaiian hotspot. At the top of the lower mantle, plumes with large viscosity variations have high‐velocity conduits 50–60 km in diameter and 125‐km‐diameter thermal halos, a centerline temperature anomaly of about 500 K and a centerline velocity of about 75 cm yr−1. Plumes with weak viscosity variations are approximately twice as broad and have centerline temperature anomalies less than 160 K at the same height and much smaller velocity. Large viscosity variations and a minimum heat transport are both