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Compressional and shear wave velocities (Vp, Vs) of candidate Martian deep‐mantle minerals, FeO‐rich ringwoodite ((Mg0.66Fe0.34)2SiO4) and majorite (Mg0.75Fe0.10Al0.26Ca0.07Si0.84O3), were measured up to 25 GPa and 700 K using Brillouin light scattering coupled with externally‐heated diamond anvil cells. Thermoelastic modeling of our results and literature data along a representative areotherm showed that Vp and Vs of FeO‐bearing ringwoodite are approximately 7.5% and 11.0% higher than that of the majorite. Our results reveal that velocity profiles of these Martian deep‐mantle minerals are more sensitive to variations in the ringwoodite/majorite (Mg/Si) ratio than to thermal and FeO chemical perturbations. Our best‐fit velocity model to a recent seismic model by Samuel et al. (2023, ) indicates the Martian mantle contains approximately 67 vol.% ringwoodite and 33 vol.% majorite, suggesting a ringwoodite‐rich aggregate in the Martian lowermost solid mantle. The ringwoodite‐majorite mantle likely co‐evolved with the FeO and other incompatible elements in the molten silicate layer above the Martian core‐mantle boundary.

The properties and relative stability of different structures of iron at the extreme conditions of pressure and temperature of relevance for the Earth's core were determined with ab‐initio atomistic simulations aided by a machine‐learning force‐field. We find that the body‐centered cubic (bcc) structure is mechanically stable at core temperatures, but its free energy is marginally higher than those of the hexagonal close‐packed and face‐centered cubic structures. The bcc structure is the only structure whose shear sound velocity matches seismic data. The small free‐energy difference between competing structures suggests that the role of impurities could be crucial in stabilizing the bcc structure in the inner core. Plain Language Summary Determining the crystal structure and the elastic properties of the compound that forms the Earth's solid inner core is crucial to interpret seismic data. We know that the inner core is predominantly composed of iron, but laboratory‐based experiments and theoretical modeling haven't yet been able to constrain the crystal structure and the properties of pure Fe at the conditions of pressure and temperature found in the inner core. We have recently developed a deep‐learning‐aided atomistic simulation method that is able to determine Gibbs free energies of solids with quantum‐chemical accuracy (a few meV/atom). We find that although body‐centered cubic Fe is energetically slightly less favored than the hexagonal close‐packed form, the shear wave velocity of bcc Fe matches seismic data much better than all other crystal structures, suggesting that bcc is a strong candidate for the crystal structure of Fe in the Earth's inner core and could be stabilized by the presence of light elements in the core. Key Points The body‐centered cubic structure of iron is mechanically stable at inner core conditions The hexagonal close‐packed structure is more stable, but small free energy differences could allow impurities to reverse this stability The observed low shear velocity in the Earth's inner core is likely to be caused by the presence of the body‐centered cubic phase

The absence of sound‐velocity data spanning the entire lower mantle pressures for (Fe, Al)‐bearing bridgmanite impedes direct comparisons with seismic wave observations, leaving the chemistry of the lower mantle unresolved. The present ultra‐high pressure sound‐velocity measurements of in situ synthesized (Fe, Al)‐bearing bridgmanite up to 130 GPa indicate that a substantial portion of iron in it originally synthesized from a glass with ferrous (Fe2+) iron becomes ferric (Fe3+). Furthermore, its shear wave velocity profile shows a considerable reduction of approximately 1.6%–2.2% on average when compared to MgSiO3 across the lower mantle. These results indicate that the lower mantle highly enriched with ferric iron‐rich bridgmanite comprising with greater than 95 vol% of the lower mantle, implying that the lower mantle is significantly rich in silica with a Mg/Si ratio approaching 1, compared to the upper mantle (Mg/Si ∼ 1.3), which supports the layered convection model securing the primordial chemical distinction.

Compressional and shear wave velocities of polycrystalline stishovite (SiO2) have been measured at simultaneous high pressures and temperatures up to 14.5 GPa and 800°C. By fitting velocities to the finite strain equations, the elastic moduli and density were determined to be KS0 = 306.6(46) GPa, KS′ = 4.92(10), ∂KS/∂T = −0.024(1) GPa/K, G0 = 229.0(34) GPa, G′ = 1.07(10), ∂G/∂T = −0.017(1) GPa/K, ρ0 = 4.287(2) g/cm3. Our modeling suggested that, in the eclogite, coesite‐stishovite transition can increase P and S wave velocities by 2.4% and 3.5%, respectively. A comparison between geophysical observations and our model shows that the coesite‐stishovite phase transition in the eclogite can potentially be responsible for the occurrence of the X discontinuity beneath Hawaii. In addition, our current results suggest an eclogite‐rich layer between 340 and 450 km depth beneath Hawaii. The eclogite concentration at the top and bottom of the layer is 41–55 vol% and >77 vol%, respectively. Plain Language Summary In this study, we investigated the elastic behavior of stishovite, a high‐pressure mineral found in subducted oceanic crust, under simultaneous high pressure and high temperature. By measuring compressional and shear wave velocities of polycrystalline stishovite at pressures up to 14.5 GPa and temperatures up to 800°C, we determined elastic modulus for stishovite. Using current data, we developed a model to predict seismic wave velocities changes in the subducted oceanic crust known as eclogite. According to our model, the coesite‐stishovite phase transition can lead to a 2.4% and 3.5% increase in P and S wave velocities of eclogite, respectively. In addition, we compared it with geophysical observations, particularly focusing on the X discontinuity beneath Hawaii. Our result indicates the presence of an eclogite‐rich layer beneath Hawaii, extending from 340 to 450 km in depth. The concentration of eclogite at the top and bottom of this layer varies, with values ranging from 41% to 55% at approximately 336 km and exceeding 77% at around 448 km depth. Key Points Direct measurement of P and S wave velocities of stishovite at mantle pressures and temperatures In the eclogite, coesite‐stishovite transition can result in seismically detectable first order increase in P and S velocities An eclogite‐rich layer model can interpret the seismic X‐discontinuity in Hawaii area

It has been hypothesized that submesoscale flows play an important role in the vertical transport of climatically important tracers, due to their strong associated vertical velocities. However, the multi-scale, non-linear, and Lagrangian nature of transport makes it challenging to attribute proportions of the tracer fluxes to certain processes, scales, regions, or features. Here we show that criteria based on the surface vorticity and strain joint probability distribution function (JPDF) effectively decomposes the surface velocity field into distinguishable flow regions, and different flow features, like fronts or eddies, are contained in different flow regions. The JPDF has a distinct shape and approximately parses the flow into different scales, as stronger velocity gradients are usually associated with smaller scales. Conditioning the vertical tracer transport on the vorticity-strain JPDF can therefore help to attribute the transport to different types of flows and scales. Applied to a set of idealized Antarctic Circumpolar Current simulations that vary only in horizontal resolution, this diagnostic approach demonstrates that small-scale strain dominated regions that are generally associated with submesoscale fronts, despite their minuscule spatial footprint, play an outsized role in exchanging tracers across the mixed layer base and are an important contributor to the large-scale tracer budgets. Resolving these flows not only adds extra flux at the small scales, but also enhances the flux due to the larger-scale flows.

Point-particle direct numerical simulations have been employed to quantify the turbulence modulation and particle responses in a turbulent particle-laden jet in the two-way coupled regime with an inlet Reynolds number based on bulk velocity and jet diameter $({D_j})$ of ~10 000. The investigation focuses on three cases with inlet bulk Stokes numbers of 0.3, 1.4 and 11.2. Special care is taken to account for the particle–gas slip velocity and non-uniform particle concentrations at the nozzle outlet, enabling a reasonable prediction of particle velocity and concentration fields. Turbulence modulation is quantified by the variation of the gas-phase turbulent kinetic energy (TKE). The presence of the particle phase is found to damp the gas-phase TKE in the near-field region within $5{D_j}$ from the inlet but subsequently increases the TKE in the intermediate region of (5–20)Dj. An analysis of the gas-phase TKE transport equation reveals that the direct impact of the particle phase is to dissipate TKE via the particle-induced source term. However, the finite inertia of the particle phase affects the gas-phase velocity gradients, which indirectly affects the TKE production and dissipation, leading to the observed TKE attenuation and enhancement. Particle response to the gas-phase flow is quantified. Particles are found to exhibit notably stronger response to the gas-phase axial velocity than to the radial velocity. A new dimensionless figure is presented that collapses both the axial and radial components of the particle response as a function of the local Stokes number based on their respective integral length scales.

Surging debris flows are among the most destructive natural hazards, and elucidating the interaction between coarse‐grained fronts and the trailing liquefied slurry is key to understanding these flows. Here, we describe the application of high‐resolution and high‐frequency 3D LiDAR data to explore the dynamics of a debris flow at Illgraben, Switzerland. The LiDAR measurements facilitate automated detection of features on the flow surface, and construction of the 3D flow depth and velocity fields through time. Measured surface velocities (2–3 m s−1) are faster than front velocities (0.8–2 m s−1), illustrating the mechanism whereby the flow front is maintained along the channel. Further, we interpret the relative velocity of different particles to infer that the vertical velocity profile varies between plug flow and one that features internal shear. Our measurements provide unique insights into debris‐flow motion, and provide the foundation for a more detailed understanding of these hazardous events. Plain Language Summary Debris flows are surging flows of soil, wood, and water that can impact people and infrastructure far downstream of their initiation zone. Work by others has identified that debris flows tend to develop a distinct segregation between large particles concentrated at the front of the flow and small particles at the tail; however, the formation process and implications of this for debris‐flow motion have remained vague. In this work, we present measurements from laser scanners, originally developed for autonomous vehicles, that provide insight into this process. The scanners provide 10 scans per second, which can be used to measure the velocity of objects (rocks and woody debris) on the surface of the flow. We show that different objects in the flow move at different speeds, which results in many destructive features of debris flows. These measurements, and the resulting process understanding, are important for predicting debris‐flow hazard and reducing the associated risk. Key Points High‐resolution 3D LiDAR scans at subsecond intervals demonstrate a novel method for exploring debris‐flow dynamics LiDAR‐derived front and surface velocities allow identification of processes forming and maintaining the debris‐flow front Observations of individual particle motion place constraints on the vertical velocity profile and temporal variation in flow regimes

This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, we can consider solutions such that the curvature of the initial free surface does not belong to The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. We first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then we use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.