SUMMARY Mantle convection and long-term lithosphere dynamics in the Earth and other planets can be treated as the slow deformation of a highly viscous fluid, and as such can be described using the compressible Navier–Stokes equations. Since on Earth-sized planets the influence of compressibility is not a dominant effect, density deviations from a reference profile are at most on the order of a few percent and using the full governing equations poses numerical challenges, most modelling studies have simplified the governing equations. Common approximations assume a temporally constant, but depth-dependent reference profile for the density (the anelastic liquid approximation), or drop compressibility altogether and use a constant reference density (the Boussinesq approximation). In most previous studies of mantle convection and crustal dynamics, one can assume that the error introduced by these approximations was small compared to the errors that resulted from poorly constrained material behaviour and limited numerical accuracy. However, as model parametrizations have become more realistic, and model resolution has improved, this may no longer be the case and the error due to using simplified conservation equations might no longer be negligible: while such approximations may be reasonable for models of mantle plumes or slabs traversing the whole mantle, they may be unsatisfactory for layered materials experiencing phase transitions or materials undergoing significant heating or cooling. For example, at boundary layers or close to dynamically changing density gradients, the error arising from the use of the aforementioned compressibility approximations can be the dominant error source, and common approximations may fail to capture the physical behaviour of interest. In this paper, we discuss new formulations of the continuity equation that include dynamic density variations due to temperature, pressure and composition without using a reference profile for the density. We quantify the improvement in accuracy relative to existing formulations in a number of benchmark models and evaluate for which practical applications these effects are important. Finally, we consider numerical aspects of the new formulations. We implement and test these formulations in the freely available community software aspect, and use this code for our numerical experiments.
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An entropy method for geodynamic modelling of phase transitions: capturing sharp and broad transitions in a multiphase assemblage
Phase transitions play an important role for the style of mantle convection. While observations and theory agree that a substantial fraction of subducted slabs and rising plumes can move through the whole mantle at present day conditions, this behaviour may have been different throughout Earth’s history. Higher temperatures, such as in the early Earth, cause different phase transitions to be dominant, and also reduce mantle viscosity, favouring a more layered style of convection induced by phase transitions. A period of layered mantle convection in Earth’s past would have significant implications for the secular evolution of the mantle temperature and the mixing of mantle heterogeneities. The transition from layered to whole mantle convection could lead to a period of mantle avalanches associated with a dramatic increase in magmatic activity. Consequently, it is important to accurately model the influence of phase transitions on mantle convection. However, existing numerical methods generally preclude modelling phase transitions that are only present in a particular range of pressures, temperatures or compositions, and they impose an artificial lower limit on the thickness of phase transitions. To overcome these limitations, we have developed a new numerical method that solves the energy equation for entropy instead of temperature. This technique allows for robust coupling between thermodynamic and geodynamic models and makes it possible to model realistically sharp phase transitions with a wide range of properties and dynamic effects on mantle processes. We demonstrate the utility of our method by applying it in regional and global convection models, investigating the effect of individual phase transitions in the Earth’s mantle with regard to their potential for layering flow. We find that the thickness of the phase transition has a bigger influence on the style of convection than previously thought: with all other parameters being the same, a thin phase transition can induce fully layered convection where a broad phase transition would lead to whole-mantle convection. Our application of the method to convection in the early Earth illustrates that endothermic phase transitions may have induced layering for higher mantle temperatures in the Earth’s past.
more » « less- NSF-PAR ID:
- 10370703
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Geophysical Journal International
- Volume:
- 231
- Issue:
- 3
- ISSN:
- 0956-540X
- Page Range / eLocation ID:
- p. 1833-1849
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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SUMMARY Stagnant-lid convection, where subduction and surface plate motion is absent, is common among the rocky planets and moons in our solar system, and likely among rocky exoplanets as well. How stagnant-lid planets thermally evolve is an important issue, dictating not just their interior evolution but also the evolution of their atmospheres via volcanic degassing. On stagnant-lid planets, the crust is not recycled by subduction and can potentially grow thick enough to significantly impact convection beneath the stagnant lid. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a buoyant crustal layer. We systematically vary the crustal layer thickness, crustal layer density, Rayleigh number and Frank–Kamenetskii parameter for viscosity to map out system behaviour and determine the new scaling laws. We find two end-member regimes of behaviour: a ‘thin crust limit’, where convection is largely unaffected by the presence of the crust, and the thickness of the lithosphere is approximately the same as it would be if the crust were absent; and a ‘thick crust limit’, where the crustal thickness itself determines the lithospheric thickness and heat flux. Scaling laws for both limits are developed and fit the numerical model results well. Applying these scaling laws to rocky stagnant-lid planets, we find that the crustal thickness needed for convection to enter the thick crust limit decreases with increasing mantle temperature and decreasing mantle reference viscosity. Moreover, if crustal thickness is limited by the formation of dense eclogite, and foundering of this dense lower crust, then smaller planets are more likely to enter the thick crust limit because their crusts can grow thicker before reaching the pressure where eclogite forms. When convection is in the thick crust limit, mantle heat flux is suppressed. As a result, mantle temperatures can be elevated by 100 s of degrees K for up to a few Gyr in comparison to a planet with a thin crust. Whether convection enters the thick crust limit during a planet’s thermal evolution also depends on the initial mantle temperature, so a thick, buoyant crust additionally acts to preserve the influence of initial conditions on stagnant-lid planets for far longer than previous thermal evolution models, which ignore the effects of a thick crust, have found.more » « less
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PhD Dissertation Abstract: The imposing andesite stratovolcano is the characteristic expression of subduction zone magmatism, posing hazards to coastal populations and bearing insight into deep Earth processes. On a map of a typical volcanic arc, one can easily distinguish the approximately linear alignment and regular spacing of these major edifices that stand out from a diffuse distribution of mafic volcanoes (e.g. the Quaternary Cascades; Hildreth, 2007). The andesitic composite volcanoes have a reputation for being complex, open systems: crystal zoning “stratigraphies,” diverse crystal cargoes including antecrysts or xenocrysts, quenched magmatic inclusions, and variations in isotopic signatures are among the many lines of evidence that these systems involve a variety of igneous processes and melt sources. 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The two groups are recurrent through time and with no geographic distinction; in fact, both types were tapped by the Hogback Mountain volcano. Together both of these groups, alongside CABs from Mount Adams and various basalts from Mount St. Helens, form a compositional array between the basalts of the High Cascades and the intraplate-type basalts (IPB) of Mount Adams and Simcoe volcanic field. These results lead to three conclusions. 1) Variably subduction-modified mantle is distributed across the region, perhaps either as stratified layers or a web-like network of fluid pathways amongst less metasomatized mantle. 2) Transitional compositions between the IPBs and typical “High Cascades” CAB/HAOT signature suggest a broader influence of the mantle domain that feeds IPBs—if asthenospheric mantle through a slab window, as suggested by Mullen et al. (2017), then perhaps it bleeds in smaller quantities over a broader area. 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