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| Titel |
Advancing dynamic and thermodynamic modelling of magma oceans |
| VerfasserIn |
Dan Bower, Aaron Wolf, Patrick Sanan, Paul Tackley |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250140624
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| Publikation (Nr.) |
 EGU/EGU2017-4038.pdf |
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| Zusammenfassung |
| The techniques for modelling low melt-fraction dynamics in planetary interiors are
well-established by supplementing the Stokes equations with Darcy’s Law. But modelling
high-melt fraction phenomena, relevant to the earliest phase of magma ocean cooling,
necessitates parameterisations to capture the dynamics of turbulent flow that are otherwise
unresolvable in numerical models. Furthermore, it requires knowledge about the material
properties of both solid and melt mantle phases, the latter of which are poorly described by
typical equations of state. To address these challenges, we present (1) a new interior evolution
model that, in a single formulation, captures both solid and melt dynamics and hence charts
the complete cooling trajectory of a planetary mantle, and (2) a physical and intuitive
extension of a “Hard Sphere” liquid equation of state (EOS) to describe silicate melt
properties for the pressure-temperature (P-T) range of Earth’s mantle. Together, these two
advancements provide a comprehensive and versatile modelling framework for probing the
far-reaching consequences of magma ocean cooling and crystallisation for Earth and other
rocky planets.
The interior evolution model accounts for heat transfer by conduction, convection, latent
heat, and gravitational separation. It uses the finite volume method to ensure energy
conservation at each time-step and accesses advanced time integration algorithms by
interfacing with PETSc. This ensures it accurately and efficiently computes the dynamics
throughout the magma ocean, including within the ultra-thin thermal boundary layers (< 2
cm thickness) at the core-mantle boundary and surface. PETSc also enables our code
to support a parallel implementation and quad-precision calculations for future
modelling capabilities. The thermodynamics of mantle melting are represented using a
pseudo-one-component model, which retains the simplicity of a standard one-component
model while introducing a finite temperature interval for melting (important for
multi-component systems). Our new high P-T liquid EOS accurately captures the energetics
and physical properties of the partially molten system whilst retaining the largest number of
familiar EOS parameters.
We demonstrate the power of our integrated dynamic and EOS model by exploring
two crystallisation scenarios for Earth that are dictated by the coincidence of the
liquid adiabat and melting curve. Experiments on melting of primitive chondrite
composition predict that crystallisation occurs from the “bottom-up”, whereas molecular
dynamics simulations of MgSiO3 perovskite suggest crystallisation occurs from the
“middle-out”. In each case, we evaluate the lifetime of the magma ocean using our
model and find that in both scenarios, initial cooling is rapid and the rheological
transition (boundary between melt- and solid-like behaviour) is reached within a
few kyrs. During this stage efficient mixing prevents the establishment of thermal
and chemical heterogeneity, so it may be challenging to locate a signature of the
earliest phase of magma ocean evolution. At the rheological transition, cooling is
governed by gravitational separation and viscous creep, and even in the absence of iron
partitioning our models predict long-lasting (> 500 Myr) melt at the base of the mantle. |
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