arXiv subjects

Renaud Deguen

Publications and source records attributed to Renaud Deguen.

13 recordsLinked to original sources

arXiv2026

Ohmic and viscous damping of inner core translational oscillations

Large earthquakes can trigger translational oscillations of Earth's inner core (Slichter modes), yet their damping remains uncertain. Using simulations, we quantify viscous and Ohmic dissipation in the fluid outer core. Earth's rotation splits the motion into one polar and two equatorial modes. We explore all three and derive scaling laws for the quality factor with each dissipation mechanism. Viscous effects are negligible, confined to a thin layer at the inner core boundary. Ohmic dissipation dominates, with decay times of 3-16 years. Equatorial modes damp at least twice as fast as the polar mode. Our results suggest that Slichter modes can persist for years. Their continued non-detection is therefore more likely due to weak excitation than rapid damping.

physics.geo-ph↗

arXiv2025

On the concentration distribution in turbulent thermals

Turbulent thermals emerge in a wide variety of geophysical and industrial flows, such as atmospheric cumulus convection and pollutant dispersal in oceans and lakes. When a buoyant fluid mass rises, or sinks, heat and mass transfers occur by the engulfment of the fresh surrounding fluid inside the thermal - a process that spans over multiple scales from macroscopic entrainment of ambient fluid to microscopic diffusive processes. Turbulent thermals are typically investigated through their integral properties (radius, depth, entrainment rate). However, mixing processes depend on the internal distribution of concentration or temperature inside a thermal, which remains poorly constrained. Here, we use laboratory fluid dynamics experiments and direct numerical simulations to investigate the mixing of a passive scalar in turbulent thermals with large Reynolds numbers. We track the evolution of the concentration field, computing its moments and the probability density function. The concentration distribution exhibits self-similarity over time, except at high concentrations, possibly because of the presence of undiluted cores. These distributions are well approximated by an exponential probability density function. Although diffusion has a strong effect on the spatial structure of the concentration field, we observe no significant effect of diffusivity on the concentration distributions in the investigated range of Peclet numbers.

physics.flu-dyn↗

arXiv2023

Velocity field and cavity dynamics in drop impact experiments

Drop impact experiments allow the modelling of a wide variety of natural processes, from raindrop impacts to planetary impact craters. In particular, interpreting the consequences of planetary impacts requires an accurate description of the flow associated with the cratering process. In our experiments, we release a liquid drop above a deep liquid pool to investigate simultaneously the dynamics of the cavity and the velocity field produced around the air-liquid interface. Using particle image velocimetry, we analyse quantitatively the velocity field using a shifted Legendre polynomial decomposition. We show that the velocity field is more complex than considered in previous models, in relation to the non-hemispherical shape of the crater. In particular, the velocity field is dominated by degrees 0 and 1, with contributions from degree 2, and is independent of the Froude and the Weber numbers when these numbers are large enough. We then derive a semi-analytical model based on the Legendre polynomial expansion of an unsteady Bernoulli equation coupled with a kinematic boundary condition at the crater boundary. This model explains the experimental observations and can predict the time evolution of both the velocity field and the shape of the crater, including the initiation of the central jet.

physics.flu-dyn↗

arXiv2019

Fluid Dynamics of Earth's core: geodynamo, inner core dynamics, core formation

This chapter is build from three 1.5 hours lectures given in Udine in april 2018 on various aspects of Earth's core dynamics. The chapter starts with a short historical note on the discovery of Earth's magnetic field and core (section 1). We then turn to an introduction of magnetohydrodynamics (section 2), introducing and discussing the induction equation and the form and effects of the Lorentz force. Section 3 is devoted to the description of Earth's magnetic field, introducing its spherical harmonics description and showing how it can be used to demonstrate the internal origin of the geomagnetic origin. We then move to an introduction of the convection-driven model of the geodynamo (section 4), discussing our current understanding of the dynamics of Earth's core, obtaining heuristically the Ekman dependency of the critical Rayleigh number for natural rotating convection, and introducing the equations and non-dimensional parameters used to model a convectively driven dynamo. The following section deals with the energetics of the geodynamo (section 5). The final two section deal with the dynamics of the inner core, focusing on the effect of the magnetic field (section 6), and with the formation of the core (section 7). Given the wide scope of this chapter and the limited time available, this introduction to Earth's core dynamics is by no means intended to be comprehensive. For more informations, the interested reader may refer to Jones (2011), Olson (2013), or Christensen and Wicht (2015) on the geomagnetic field and the geodynamo, to Sumita and Bergman (2015), Deguen (2012) and Lasbleis and Deguen (2015) on the dynamics of the inner core, and to Rubie et al. (2015) on core formation.

physics.geo-ph↗

arXiv2019

Experimental study of convection in the compressible regime

An experiment of thermal convection with significant compressible effects is presented. The high-gravity environment of a centrifuge and the choice of xenon gas enable us to observe an average adiabatic temperature gradient up to 3.5 K cm$^{-1}$ over a 4 cm high cavity. At the highest rotation rate investigated, 9990 rpm, the superadiabatic temperature difference applied to the gas layer is less than the adiabatic temperature difference. The convective regime is characterized by a large Rayleigh number, about 10$^{12}$, and dominant Coriolis forces (Ekman number of order 10$^{-6}$). The analysis of temperature and pressure fluctuations in our experiments shows that the dynamics of the flow is in a quasi-geostrophic regime. Still, a classical power law (exponent 0.3 $\pm$ 0.04) is observed between the Nusselt number (dimensionless heat flux) and the superadiabatic Rayleigh number (dimensionless superadiabatic temperature difference). However, a potential hysteresis is seen between this classical high flux regime and a lower heat flux regime. It is unclear whether this is due to compressible or Coriolis effects. In the transient regime of convection from an isothermal state, we observe a local decrease of temperature which can only be explained by adiabatic decompression.

physics.flu-dyn↗

arXiv2018

Small-Scale Metal/Silicate Equilibration During Core Formation: The Influence of Stretching Enhanced Diffusion on Mixing

Geochemical data provide key information on the timing of accretion and on the prevailing physical conditions during core/mantle differentiation. However, their interpretation depends critically on the efficiency of metal/silicate chemical equilibration, which is poorly constrained. Fluid dynamics experiments suggest that, before its fragmentation, a volume of liquid metal falling into a magma ocean undergoes a change of topology from a compact volume of metal toward a collection of sheets and ligaments. We investigate here to what extent the vigorous stretching of the metal phase by the turbulent flow can increase the equilibration efficiency through what is known as stretching enhanced diffusion. We obtain scaling laws giving the equilibration times of sheets and ligaments as functions of a Péclet number based on the stretching rate. At large Péclet, stretching drastically decreases the equilibration time, which in this limit depends only weakly on the diffusivity. We also perform 2D numerical simulations of the evolution of a volume of metal falling into a magma ocean, from which we identify several equilibration regimes depending on the values of the Péclet (Pe), Reynolds (Re), and Bond (Bo) numbers. At large Pe, Re and Bo, the metal phase is vigorously stretched and convoluted in what we call a stirring regime. The equilibration time is found to be independent of viscosity and surface tension and depends weakly on diffusivity. Equilibration is controlled by an efficient thermochemical stretching enhanced diffusion mechanism developing from the mean flow and entraining the surrounding silicate phase.

physics.geo-ph↗

arXiv2018

Rayleigh-Bénard convection in a creeping solid with melting and freezing at either or both its horizontal boundaries

Solid state convection can take place in the rocky or icy mantles of planetary objects and these mantles can be surrounded above or below or both by molten layers of similar composition. A flow toward the interface can proceed through it by changing phase. This behaviour is modeled by a boundary condition taking into account the competition between viscous stress in the solid, that builds topography of the interface with a timescale $τ_η$, and convective transfer of the latent heat in the liquid from places of the boundary where freezing occurs to places of melting, which acts to erase topography, with a timescale $τ_ϕ$. The ratio $Φ=τ_ϕ/τ_η$ controls whether the boundary condition is the classical non-penetrative one ($Φ\rightarrow \infty$) or allows for a finite flow through the boundary (small $Φ$). We study Rayleigh-Bénard convection in a plane layer subject to this boundary condition at either or both its boundaries using linear and weakly non-linear analyses. When both boundaries are phase change interfaces with equal values of $Φ$, a non-deforming translation mode is possible with a critical Rayleigh number equal to $24Φ$. At small values of $Φ$, this mode competes with a weakly deforming mode having a slightly lower critical Rayleigh number and a very long wavelength, $λ_c\sim 8\sqrt{2}π/ 3\sqrtΦ$. Both modes lead to very efficient heat transfer, as expressed by the relationship between the Nusselt and Rayleigh numbers. When only one boundary is subject to a phase change condition, the critical Rayleigh number is $\Ray_c=153$ and the critical wavelength is $λ_c=5$. The Nusselt number increases about twice faster with Rayleigh number than in the classical case with non-penetrative conditions when the bottom boundary is a phase change interface.

physics.flu-dyn↗

arXiv2014

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.

physics.flu-dyn↗

arXiv2014

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

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 what has usually been assumed, 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, a much smaller re-equilibration degree is predicted in the case of large impacts for which the impactor core diameter approaches the magma ocean thickness.

physics.geo-ph↗

arXiv2013

Thermal convection in Earth's inner core with phase change at its boundary

Inner core translation, with solidification on one hemisphere and melting on the other, provides a promising basis for understanding the hemispherical dichotomy of the inner core, as well as the anomalous stable layer observed at the base of the outer core - the F-layer - which might be sustained by continuous melting of inner core material. In this paper, we study in details the dynamics of inner core thermal convection when dynamically induced melting and freezing of the inner core boundary (ICB) are taken into account. If the inner core is unstably stratified, linear stability analysis and numerical simulations consistently show that the translation mode dominates only if the viscosity $η$ is large enough, with a critical viscosity value, of order $3 10^{18}$ Pas, depending on the ability of outer core convection to supply or remove the latent heat of melting or solidification. If $η$ is smaller, the dynamical effect of melting and freezing is small. Convection takes a more classical form, with a one-cell axisymmetric mode at the onset and chaotic plume convection at large Rayleigh number. [...] Thermal convection requires that a superadiabatic temperature profile is maintained in the inner core, which depends on a competition between extraction of the inner core internal heat by conduction and cooling at the ICB. Inner core thermal convection appears very likely with the low thermal conductivity value proposed by Stacey & Davis (2007), but nearly impossible with the much higher thermal conductivity recently put forward. We argue however that the formation of an iron-rich layer above the ICB may have a positive feedback on inner core convection: it implies that the inner core crystallized from an increasingly iron-rich liquid, resulting in an unstable compositional stratification which could drive inner core convection, perhaps even if the inner core is subadiabatic.

physics.geo-ph↗

arXiv2013

Thermal convection in a spherical shell with melting/freezing at either or both of its boundaries

In a number of geophysical or planetological settings (Earth's inner core, a silicate mantle crystallizing from a magma ocean, or an ice shell surrounding a deep water ocean) a convecting crystalline layer is in contact with a layer of its melt. Allowing for melting/freezing at one or both of the boundaries of the solid layer is likely to affect the pattern of convection in the layer. We study here the onset of thermal convection in a viscous spherical shell with dynamically induced melting/freezing at either or both of its boundaries. It is shown that the behavior of each interface depends on the value of a dimensional number P, which is the ratio of a melting/freezing timescale over a viscous relaxation timescale. A small value of P corresponds to permeable boundary conditions, while a large value of P corresponds to impermeable boundary conditions. The linear stability analysis predicts a significant effect of semi-permeable boundaries when the number P characterizing either of the boundary is small enough: allowing for melting/freezing at either of the boundary results in the emergence of larger scale convective modes. The effect is particularly drastic when the outer boundary is permeable, since the degree 1 mode remains the most unstable even in the case of thin spherical shells. In the case of a spherical shell with permeable inner and outer boundaries, the most unstable mode consists in a global translation of the solid shell, with no deformation. In the limit of a full sphere with permeable outer boundary, this corresponds to the "convective translation" mode recently proposed for Earth's inner core. As an example of possible application, we discuss the case of thermal convection in Enceladus' ice shell assuming the presence of a global subsurface ocean, and found that melting/freezing could have an important effect on the pattern of convection in the ice shell.

physics.geo-ph↗

arXiv2012

Melting-induced stratification above the Earth's inner core due to convective translation

In addition to its global North-South anisotropy(1), there are two other enigmatic seismological observations related to the Earth's inner core: asymmetry between its eastern and western hemispheres(2-6) and the presence of a layer of reduced seismic velocity at the base of the outer core(6-12). This 250-km-thick layer has been interpreted as a stably stratified region of reduced composition in light elements(13). Here we show that this layer can be generated by simultaneous crystallization and melting at the surface of the inner core, and that a translational mode of thermal convection in the inner core can produce enough melting and crystallization on each hemisphere respectively for the dense layer to develop. The dynamical model we propose introduces a clear asymmetry between a melting and a crystallizing hemisphere which forms a basis for also explaining the East-West asymmetry. The present translation rate is found to be typically 100 million years for the inner core to be entirely renewed, which is one to two orders of magnitude faster than the growth rate of the inner core's radius. The resulting strong asymmetry of buoyancy flux caused by light elements is anticipated to have an impact on the dynamics of the outer core and on the geodynamo.

physics.geo-ph↗

arXiv2008

On the existence and structure of a mush at the inner core boundary of the Earth

It has been suggested about 20 years ago that the liquid close to the inner core boundary (ICB) is supercooled and that a sizable mushy layer has developed during the growth of the inner core. The morphological instability of the liquid-solid interface which usually results in the formation of a mushy zone has been intensively studied in metallurgy, but the freezing of the inner core occurs in very unusual conditions: the growth rate is very small, and the pressure gradient has a key role, the newly formed solid being hotter than the adjacent liquid. We investigate the linear stability of a solidification front under such conditions, pointing out the destabilizing role of the thermal and solutal fields, and the stabilizing role of the pressure gradient. The main consequence of the very small solidification rate is the importance of advective transport of solute in liquid, which tends to remove light solute from the vicinity of the ICB and to suppress supercooling, thus acting against the destabilization of the solidification front. For plausible phase diagrams of the core mixture, we nevertheless found that the ICB is likely to be morphologically unstable, and that a mushy zone might have developed at the ICB. The thermodynamic thickness of the resulting mushy zone can be significant, from $\sim100$ km to the entire inner core radius, depending on the phase diagram of the core mixture. However, such a thick mushy zone is predicted to collapse under its own weight, on a much smaller length scale ($\lesssim 1$ km). We estimate that the interdendritic spacing is probably smaller than a few tens of meter, and possibly only a few meters.

physics.geo-ph↗