Maylis Landeau

Turbulent metal–silicate mixing, fragmentation, and equilibration in magma oceans

Abstract Much of the Earth was built by high-energy impacts of planetesimals and embryos, many of these impactors already differentiated, with metallic cores of their own. Geochemical data provide critical information on the timing of accretion and the prevailing physical conditions, but their interpretation depends critically on the degree of metal–silicate chemical equilibration during core–mantle differentiation, which is poorly constrained. Efficient equilibration requires that the large volumes of iron derived from impactor cores mix with molten silicates down to scales small enough to allow fast metal–silicate mass transfer. Here we use fluid dynamics experiments to show that large metal blobs falling in a magma ocean mix with the molten silicate through turbulent entrainment, with fragmentation into droplets eventually resulting from the entrainment process. In our experiments, fragmentation of the dense fluid occurs after falling a distance equal to 3–4 times its initial diameter, at which point a sizable volume of ambient fluid has already been entrained and mixed with the dense falling fluid. Contrary to previous assumptions, we demonstrate that fragmentation of the metallic phase into droplets may not be required for efficient equilibration: turbulent mixing, by drastically increasing the metal–silicate interfacial area, may result in fast equilibration even before fragmentation. Efficient re-equilibration is predicted for impactors of size small compared to the magma ocean depth. In contrast, much less re-equilibration is predicted for large impacts in situations where the impactor core diameter approaches the magma ocean thickness.

Performance benchmarks for a next generation numerical dynamo model

Numerical simulations of the geodynamo have successfully represented many observable characteristics of the geomagnetic field, yielding insight into the fundamental processes that generate magnetic fields in the Earths core. Because of limited spatial resolution, however, the diffusivities in numerical dynamo models are much larger than those in the Earths core, and consequently, questions remain about how realistic these models are. The typical strategy used to address this issue has been to continue to increase the resolution of these quasi-laminar models with increasing computational resources, thus pushing them toward more realistic parameter regimes. We assess which methods are most promising for the next generation of supercomputers, which will offer access to O(106) processor cores for large problems. Here we report performance and accuracy benchmarks from 15 dynamo codes that employ a range of numerical and parallelization methods. Computational performance is assessed on the basis of weak and strong scaling behavior up to 16,384 processor cores. Extrapolations of our weak-scaling results indicate that dynamo codes that employ two-dimensional or three-dimensional domain decompositions can perform efficiently on up to ∼106 processor cores, paving the way for more realistic simulations in the next model generation.

Experiments on the fragmentation of a buoyant liquid volume in another liquid

We present experiments on the instability and fragmentation of volumes of heavier liquid released into lighter immiscible liquids. We focus on the regime defined by small Ohnesorge numbers, density ratios of order one, and variable Weber numbers. The observed stages in the fragmentation process include deformation of the released fluid by either Rayleigh-Taylor instability or vortex ring roll-up and destabilization, formation of filamentary structures, capillary instability, and drop formation. At low and intermediate Weber numbers, a wide variety of fragmentation regimes is identified. Those regimes depend on early deformations, which mainly result from a competition between the growth of Rayleigh-Taylor instabilities and the roll-up of a vortex ring. At high Weber numbers, turbulent vortex ring formation is observed. We have adapted the standard theory of turbulent entrainment to buoyant vortex rings with initial momentum. We find consistency between this theory and our experiments, indicating that the concept of turbulent entrainment is valid for non-dispersed immiscible fluids at large Weber and Reynolds numbers.

Outer Core Stratification From the High Latitude Structure of the Geomagnetic Field

The presence of stable stratification has broad implications for the thermal and compositional state of the outer core, the evolution of Earths deep interior, and the energetics of the geodynamo. Yet the origin, strength, and depth extent of stratification in the region below the core-mantle boundary remain open questions. Here we compare magnetic fields produced by numerical dynamos that include heterogeneous stable thermal stratification below their outer boundary with models of the geomagnetic field on the core-mantle boundary, focusing on high latitude structures. We demonstrate that the combination of high magnetic field intensity regions and reversed magnetic flux spots, especially at high latitudes, constrains outer core stratification below the core-mantle boundary. In particular, we find that the negative contribution to the axial dipole from reversed flux spots is a strong inverse function of the stratification. Comparison of our numerical dynamo results to the structure of the historical geomagnetic field suggests up to 400 km of permeable, laterally heterogeneous thermal stratification below the core-mantle boundary.