arXiv subjects

Stéphane Labrosse

Publications and source records attributed to Stéphane Labrosse.

7 recordsLinked to original sources

arXiv2025

Convective regimes of internally heated steady thermal convection of temperature-dependent viscous fluid

We study dynamical regimes of thermal convection with temperature-dependent viscosity driven by homogeneous internal heating. Two-dimensional steady-state convective solutions with the Frank-Kamenetskii viscosity are obtained by the Newton method for a number of different values of the Rayleigh number and the strength of the dependence of the viscosity on temperature. By classifying the solutions with the top surface mobility, we find the sluggish lid regime between the mobile and stagnant lid regimes. The solutions of the sluggish regime are characterized by a large viscosity contrast through the boundary layer below the conductive lid and a rapid increase of the Nusselt number with respect to the Rayleigh number. For most solutions in the mobile and stagnant lid regimes, the Nusselt number is proportional to the 1/6 power of the Rayleigh number, which can be derived by taking into account the effect of thin and strong downwelling plumes. Time evolution calculations show that the steady solutions become unstable for large Rayleigh numbers, where additional downward plumes grow on the background convective flows. This can be explained by the timescale of the Rayleigh--Taylor instability for the thermal boundary layer between the conductive lid and the convective core, which is shorter than the timescale of horizontal advection by the background flow. In addition, steady convective solutions with Arrhenius-law viscosity are calculated for several values of the parameters. The obtained regime diagram qualitatively agrees with that of the Frank-Kamenetskii viscosity, while there is a slight difference in the locations of the regime boundaries.

physics.flu-dyn↗

arXiv2024

Geomagnetic dipole stability and zonal flows controlled by mantle heat flux heterogeneities

This work aims at acquiring a more complete understanding of how lateral heterogeneities of the CMB heat flux affect the geodynamo while other relevant parameters are pushed towards realistic values. For this purpose, we ran geodynamo simulations with degree 1 and 2 spherical harmonic patterns of heat flux at the CMB. Several geodynamo models are used, ranging from standard numerical dynamos to more extreme parameters, including strong field cases and turbulent cases. We show that heat flux heterogeneities with amplitudes compatible with our knowledge of mantle convection history can favour multipolar dynamos. The multipolar transition is associated with a disruption of westward flows either through eastward thermal winds or through a loss of equatorial symmetry. Strong field dynamo models are found to have larger westward flows and are less sensitive to heat flux heterogeneities. Furthermore, we find that the dipolar fraction of the magnetic field correlates with $M_{Za}^*=\dfrac{Λ_{Za}}{Rm_{Za}^2}$ where $Λ_{Za}$ is the zonal antisymmetric Elsasser number and $Rm_{Za}$ is the zonal antisymmetric magnetic Reynolds number. Importantly, $M_{Za}^*$ estimated for the Earth's core is consistent with a reversing dipolar magnetic field. Within the range of $M_{Za}^*$ susceptible to reversals, breaking the equatorial symmetry or forcing eastward zonal flows through an equatorial cooling of the core consistently triggers reversals or a transition towards multipolar dynamos in our simulations. Our results support that time variations of heat-flux heterogeneities driven by mantle convection through Earth's history are capable of inducing the significant variations in the reversal frequency observed in the palaeomagnetic record.

astro-ph.EP↗

arXiv2020

The Effects of Robin Boundary Condition on Thermal Convection in a Rotating Spherical Shell

Convection in a spherical shell is widely used to model fluid layers of planets and stars. The choice of thermal boundary conditions in such models is not always straightforward. To understand the implications of this choice, we report on the effects of the thermal boundary condition on thermal convection, in terms of instability onset, fully developed transport properties and flow structure. We use the Boussinesq approximation, and impose a Robin boundary condition at the top. This enforces the temperature anomaly and its radial derivative to be linearly coupled with a proportionality factor $β$. Using the height H of the fluid layer, we introduce the non-dimensional Biot number Bi* = $β$H. Varying Bi* allows us to transition from fixed temperature for Bi* = +$\infty$, to fixed thermal flux for Bi* = 0. The bottom boundary of the shell is kept isothermal. We find that the onset of convection is only affected by Bi* in the non-rotating case. Far from onset, considering an effective Rayleigh number and a generalized Nusselt number, we show that the Nusselt and P{é}clet numbers follow standard universal scaling laws, independent of Bi* in all cases considered. However, the large-scale flow structure keeps the signature of the boundary condition with more vigorous large scales for smaller Bi* , even though the global heat transfer and kinetic energy are the same. Finally, for all practical purposes, the Robin condition can be safely replaced by a fixed flux when Bi* < 0.03 and by a fixed temperature for Bi* > 30.

physics.class-ph↗

arXiv2020

Low thermal conductivity of iron-silicon alloys at Earth core conditions with implications for the geodynamo

Earth core is composed of iron (Fe) alloyed with light elements, e.g., silicon (Si). Its thermal conductivity critically affects Earth thermal structure, evolution, and dynamics, as it controls the magnitude of thermal and compositional sources required to sustain a geodynamo over Earth history. Here we directly measured thermal conductivities of solid Fe and Fe-Si alloys up to 144 GPa and 3300 K. 15 at% Si alloyed in Fe substantially reduces its conductivity by about 2 folds at 132 GPa and 3000 K. An outer core with 15 at% Si would have a conductivity of about 20 W m-1 K-1, lower than pure Fe at similar pressure-temperature conditions. This suggests a lower minimum heat flow, around 3 TW, across the core-mantle boundary than previously expected, and thus less thermal energy needed to operate the geodynamo. Our results provide key constraints on inner core age that could be older than two billion-years.

cond-mat.mtrl-sci↗

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

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

Thermal and compositional stratification of the inner core

The improvements of the knowledge of the seismic structure of the inner core and the complexities thereby revealed ask for a dynamical origin. Sub-solidus convection was one of the early suggestions to explain the seismic anisotropy, but it requires an unstable density gradient either from thermal or compositional origin, or from both. Temperature and composition profiles in the inner core are computed using a unidimensional model of core evolution including diffusion in the inner core and fractional crystallisation at the inner core boundary (ICB). The thermal conductivity of the core has been recently revised upwardly and, moreover, found to increase with depth. Values of the heat flow across the core mantle boundary (CMB) sufficient to maintain convection in the whole outer core are not sufficient to make the temperature in the inner core super-isentropic and therefore prone to thermal instability. An unreasonably high CMB heat flow is necessary to this end. The compositional stratification results from a competition of the increase of the concentration of light elements in the outer core with inner core growth, which makes the inner core concentration also increase, and of the decrease of the liquidus, which makes the partition coefficient decrease as well as the concentration of light elements in the solid. While the latter (destabilizing) effect dominates at small inner core sizes, the former takes over for a large inner core. The turnover point is encountered for an inner core about half its current size in the case of S, but much larger for the case of O. The combined thermal and compositional buoyancy is stabilizing and solid-state convection in the inner core appears unlikely, unless an early double-diffusive instability can set in.

physics.geo-ph↗