My research is currently focusing on these main topics.
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Convection from a physics point of view:
My main research interest lies on the theoretical investigation of simple convective systems with the aim to better understand planetary bodies. Various methods exist to perform a such investigation, appropriate for different types of problems. This text does not have the ambition of providing a thorough description of applied fluid mechanics. As such, I will only describe the main methods used in my work and how they can be applied.
A classical approach to characterise a convective system is to establish scaling laws. A scaling law is simply a relationship between an observable and the dimensionless numbers controlling the system. For instance, a relationship between the surface heat flux and the Rayleigh number. Significant efforts have been made to establish scaling laws for convective systems of increasing complexities. In most cases, the determination of a scaling law is conducted in two steps: (i) running a set of numerical simulations involving a large range of values for each dimensionless numbers; (ii) fitting the numerical results with a power-law relationship. A persistent issue of this method is the inherent uncertainties associated with the best-fit procedure. Because of these uncertainties, scaling laws should only be applied to systems involving dimensionless numbers within the range covered by the numerical simulations, i.e., scaling laws should only be used to interpolate the results and not to extrapolate them. To overcome this shortcoming, I developed a framework allowing to establish fully theoretical scaling laws, i.e., theoretical relationships that do not rely on a best-fit procedure. This framework has been successfully applied to a volumetrically heated system and a mixed heated system, i.e., with both internal and bottom heating.
The main interest of scaling laws is to provide a simple and quick way to estimate the thermal structure of a system. This is particularly useful to investigate problems that are out of reach of numerical simulations, for instance because they are too complex or because they are too poorly constrained. Consequently, scaling laws are widely used in Earth and planetary sciences. In my work, for instance, I used scaling laws to constrain the properties of Sputnik Planitia, a nitrogen glacier located on Pluto, and to estimate the occurrence of volcanism on exoplanets. Scaling laws can also be used in models of parameterized convection, i.e, models estimating the 1D thermal evolution of a system.
Another method to perform parameterized convection involves the use of the Mixed Length Theory (MLT). The basic idea of the MLT is to solve the energy equation by neglecting the horizontal advection of heat, while approximating the vertical advection of heat. As a result, one obtains a good estimate of the averaged temperature profile of the system, hence its surface heat flux. This theory has been found to be particularly appropriate to study the thermal evolution of turbulent systems, such as atmospheric circulation or magma ocean solidification. Nevertheless, more recently, several authors have proposed a modification of the MLT allowing to also investigate laminar systems. Building on these works, I further extended the MLT with the aim to estimate not only the averaged temperature profile but also a part of the temperature distribution. More specifically, I developed a method to constrain, at a given depth, the temperature distribution for the 5% hottest material. These constraints can then be used to assess accurately the generation of melting in models of parameterized convection.
Coworkers
- Frédéric Deschamps (IES)
- Cinzia G. Farnetani (IPGP)
- Loïc Fourel (IPGP)
- Erika Di Giuseppe (IPGP)
- Claude Jaupart (IPGP)
- Shunichi Kamata (Hokkaido University)
- Edouard Kaminski (IPGP)
- Angela Limare (IPGP)
- Camelia Neamtu (INCDTIM)
- Vasile Surducan (INCDTIM)
- Emanoil Surducan (INCDTIM)
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Thermal convection in icy satellites:
During the past four decades, space missions have gathered abundant observations of icy satellites. These observations have revealed the diversity and complexity of icy worlds, while raising a certain number of questions. One of them concerns the widespread marks of cryovolcanism observed on some icy satellites. Indeed, aqueous cryomagmas are negatively buoyant with respect to ice, so that their eruption at the surface of icy bodies cannot be due to buoyancy-driven upwelling. The mechanism at the origin of cryovolcanism remains a subject of debate. For instance, some authors have argued that the transport of melt to the surface may be due to fractional crystallisation or pressurisation of melt pockets. Interestingly, these propositions require the presence of liquid reservoirs close to the surface, which is in itself difficult to produce.
To better understand this issue, I investigated the generation of partial melting in icy shells using 3D numerical simulations of tidally heated convection conducted for a large range of parameters (Rayleigh number, tidal heating rate and viscosity contrast). The results have shown that melting may be produced within the ice layer for a large range of parameters. Interestingly, when applied to Europa, melt pockets can only be obtained for a moderate ice layer thickness, between 15 and 35 km.
The purpose of this study was also to determine the effects of melting on the thermal structure of icy shells. Indeed, because of the large lateral extent of icy shells, the investigation of their thermal evolution with 3D numerical simulations is almost impossible. One has therefore to use models of parameterized convection to understand the long-term evolution of icy satellites. However, such models are not yet available or relies on important simplifications. Building on these findings, I aim to develop models of parameterized convection appropriate for the thermal evolution of icy satellites.
Coworkers
- Frédéric Deschamps (IES)
- Gaël Choblet (LPG)
- Shunichi Kamata (Hokkaido University)
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Spin state transition, implications on mantle convection:
Since the observation by James Badro et al. (2003) of an iron spin state transition in ferropericlase, an increasing number of studies have been devoted to determine its implication. In particular, there was an apparent discrepancy between, on one side, dynamics and mineral physics studies promoting a dramatic effect of this electronic transition, and, on the other, the absence of seismic observations supporting this effect. In order to investigate this discrepancy, I considered a classical pyrolitic composition and calculated the effect of Fe2+ spin state transition in ferropericlase on density. The calculated densities agreed well with both PREM density and high pressure and temperature experiments proving the relevance of my mineralogical model. Density tables obtained with this mineralogical model have been included in a series of numerical simulations. The results have indicated a modest effect of the spin state transition on mantle dynamics solving the apparent discrepancy between mineral physics and seismological observations.
However, a potential effect of the spin state transition is to reduce the stability of LLSVPs. Yang Li has therefore included my mineralogical models in a set of spherical numerical simulations aiming to investigate the stability of these primitive reservoirs. We found (again) a modest effect of the spin state transition, since it only slightly reduces the stability of the primitive reservoirs. The chemical buoyancy ratio of the primitive material remains the dominant parameter influencing their stability.
Now, I am investigating the possible compositions explaining the seismic signature of LLSVPs. My model includes for instance the effect of alumina and involves six free parameters (proportion of bridgmanite and Ca-silicate perovskite, iron and alumina content, temperature, and oxidation state) that is allowed to vary in a large range. Preliminary results indicate that a large range of compositions may potentially explain the seismic signature of LLSVPs. Interestingly, these models involve iron contents up to 25wt% and alumina content up to 17wt%.
Coworkers
- James Badro (IPGP)
- Frédéric Deschamps (IES)
- Cinzia G. Farnetani (IPGP)
- Yang Li (CAS)
- Sang-Heon Shim (ASU)