Abstract
The Earth's mantle convects to lose heat (Holmes, 1931); doing so drives plate tectonics (Turcotte and Oxburgh, 1967). Significant gravitational energy is created by the cooling of oceanic lithosphere atop hotter, less dense mantle. When slabs subduct, this gravitational energy is mostly (~86% for whole mantle flow in a PREM-like mantle) transformed into heat by viscous dissipation. Using this perspective, we reassess the energetics of Earth’s mantle. We also reconsider the terrestrial abundances of heat producing elements U, Th, and K, and argue they are lower than previously considered and that consequently the heat produced by radioactive decay within the mantle is comparable to the present-day potential gravitational energy release by subducting slabs — both are roughly ~10-12 TW. We reassess possible core heat flow into the base of the mantle, and determine that the core may be still losing a significant amount of heat from its original formation, potentially more than the radioactive heat generation within the mantle. These factors are all likely to be important for Earth's current energetics, and argue that strong plume-driven upwelling is likely to exist within the convecting mantle.
Highlights
Roles of Gravitational Energy Transformations in Mantle ConvectionA wonderful realization of the Plate Tectonics revolution was that the surface oceanic plates form the upper thermal boundary layer of a convecting mantle (Turcotte and Oxburgh, 1967)
Summary of Core Energetics If >10–15 TW of heat loss from the core is truly needed to sustain a convective outer core geodynamo, we favor the interpretation that this is further evidence supporting our above “in-situ ICB” Clapeyron-slope estimate which suggests that the core has been cooling at a rapid rate of ∼258 K/Ga over the past 3 Ga
The initial heat for a core that has always been much hotter than overlying mantle would need to be linked to core-formation itself, either from an abundant short-lived radionuclide, or from the gravitational energy release from core segregation being preferentially concentrated into heating the growing core
Summary
A wonderful realization of the Plate Tectonics revolution was that the surface oceanic plates form the upper thermal boundary layer of a convecting mantle (Turcotte and Oxburgh, 1967). In a highly viscous fluid like the Earth’s mantle where inertial forces are negligible, the gravitational energy released from a sinking thermal density anomaly is completely transformed into viscous dissipation energy within the deforming fluid. The integral of the viscous dissipation (1st term) associated with incompressible Stokes flow is equal to the rate of gravitational energy release or gravitational power associated with rising or sinking density anomalies. For a perfectly adiabatic reference state, viscous dissipation is directly linked to gravitational power release of rising and sinking thermal density anomalies. Equation (15) states that the viscous dissipation in a compressible fluid is equal to the gravitation power released by rising or sinking thermal density anomalies. The second term in Equation (15) is commonly referred to as “adiabatic heating.” It is a historical accident that the relationship between adiabatic heating and viscous dissipation was derived by a steady-state analysis of the equation for energy conservation
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