The Current Energetics of Earth's Interior: A Gravitational Energy Perspective

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.Keywords: mantle energetics, mantle evolution, Urey ratio, gravitational potential energy, mantle secular cooling, core energetics, core secular cooling INTRODUCTION 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). When oceanic plates cool near the Earth's surface, they become denser than underlying mantle. This density contrast provides the gravitational pull that causes plates to sink when they subduct. It is perhaps most familiar to think of convection in terms of cooling-or heating-linked buoyancy forces that cause hot regions to rise and cold regions to sink within a convecting fluid. While less familiar, an equivalent way to think about these phenomena is in terms of gravitational potential energy. Both rising low-density and sinking high-density regions release gravitational potential energy. 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. For example, the Stokes problem of a sinking heavy ball in a highly viscous medium can be treated either as a force balance between the net buoyancy force on the ball and the viscous resisting force from the surrounding fluid's deformation, or as an energy balance between the gravitational energy released by the ball's sinking Morgan et al.Earth's Current Energetics and the viscous dissipation within the surrounding fluid. (In fluid dynamics, it is well-known that all slow viscous flow involves viscous friction-or viscous dissipation-that generates heat as the material strains. In this perspe...

Review article: Geothermal heat flow in Antarctica: current and future directions

“…The HPEs are incompatible with the mineral structures of the mantle so are concentrated into the crust (Boden, 2016;McDonough and Sun, 1995). Other sources of possible contributions to GHF are (1) geoneutrino emission from the mantle (Huang et al, 2013;Korenaga, 2011) and (2) gravitational pressure (Elbeze, 2013;Morgan et al, 2016).…”

“…Boreholes into submarine bedrock (34 boreholes, Supplement) have been drilled and temperature gradients measured beneath the McMurdo Sound, Amundsen Sea Embayment, and Ross Ice Shelf ( Fig. 15; Bücker et al, 2001;Decker et al, 1975;Gohl et al, 2019;McKay et al, 2018;Morin et al, 2010).…”

“…3.3). Two temperature gradients have also been measured beneath the Ross Ice Shelf (Foster, 1978; A. Burton-Johnson et al: Geothermal heat flow in Antarctica Morin et al, 2010), but otherwise heat flow beneath the Antarctic ice shelves remains poorly constrained.…”

Geothermal heat flow in Antarctica: current and future directions

“…The HPEs are incompatible with the mineral structures of the mantle, so are concentrated into the crust (Boden, 2016;McDonough and Sun, 1995). Other sources of possible contributions to GHF are: 1) geoneutrino emission from the mantle (Huang et al, 2013;Korenaga, 2011), and 2) gravitational pressure (Elbeze, 2013;Morgan et al, 2016).…”

The cross-over to magnetostrophic convection in planetary dynamo systems

“…[9]). It is presently unclear as to which buoyancy source, thermal or compositional, is the dominant convective driver [10,11]. This depends on the thermal conductivity of the core fluid [12,13], which determines how efficiently heat is conducted across the core and how much of this heat is available over to drive thermal convection in the fluid [14].…”