Periodic Reporting for period 2 - THEIA (Topographic effects in planetary fluid cores: application to the Earth-Moon system)
Período documentado: 2022-03-01 hasta 2023-08-31
Understanding planetary core flows is crucial as they generate the magnetic fields of planets and modify their rotation. However, their study is an outstanding challenge involving geomagnetism, geodesy and fluid mechanics. Notably, present models fail to explain two puzzling observations. First, geodesy constrains the Earth and Moon core dissipation to values in disagreement with those of current theoretical models. Second, lunar paleomagnetism gives an early Moon magnetic field too intense for the current planetary dynamo paradigm, based on convection.
This project tackles these issues by going beyond the present planetary core simulations, performed in exact spheres. Planetary core boundaries are actually not spherical, being affected by large-scale and small-scale deformations. This topography, although advocated for a long time to play a role for the core dynamics, has been largely overlooked in core flow models.
We will thus investigate topographic effects in planetary fluid cores by combining theory, simulations and experiments. We will build experiments to study the dissipation of turbulent flows in the presence of rotation, density variations and topography. Building upon our recent advances in applied mathematics, we will develop new numerical models to include magnetic effects in near-spherical geometries. Using efficient spectral methods, we will reach unprecedented parameters, closer to planetary ones. Developing scaling laws, we will assess how planetary core dissipation and magnetic fields are modified by topographic effects. Beyond the Earth-Moon system, these models will also apply to fluid layers of other bodies, such as the subsurface oceans of the Jupiter icy moons.
This project tackles these issues by going beyond the present planetary core simulations, performed in exact spheres. Planetary core boundaries are actually not spherical, being affected by large-scale and small-scale deformations. This topography, although advocated for a long time to play a role for the core dynamics, has been largely overlooked in core flow models.
We will thus investigate topographic effects in planetary fluid cores by combining theory, simulations and experiments. We will build experiments to study the dissipation of turbulent flows in the presence of rotation, density variations and topography. Building upon our recent advances in applied mathematics, we will develop new numerical models to include magnetic effects in near-spherical geometries. Using efficient spectral methods, we will reach unprecedented parameters, closer to planetary ones. Developing scaling laws, we will assess how planetary core dissipation and magnetic fields are modified by topographic effects. Beyond the Earth-Moon system, these models will also apply to fluid layers of other bodies, such as the subsurface oceans of the Jupiter icy moons.
During the first 30 months of the ERC project THEIA (01/09/2020 - 28/02/2023), significant progress has been made for the three work packages (WP) of the project (as detailed in the DoA), and 8 articles have been published in top-ranked international journals. In particular:
• WP1 (topography driven flows): we have obtained the mean zonal core flows due to orbital forcings (precession, tides, etc.) in deformed spherical shells (Cébron et al., J. Fluid Mech. 2021). Using a new mathematical formulation, the eigenmodes of a tidally-deformed planetary core have also been obtained, including density and pressure variations (Vidal & Cébron, Proc. R. Soc. A, 2020). Extending this new method, we have proposed a new approach to unlock the simulations of core turbulence due to orbital forcings in non-spherical geometries (which were hampered by viscous layers, see Vidal & Cébron, J. Fluid Mech. 2023).
• WP2 (interaction with buoyancy): we are currently developing a large-scale experiment, as well as a prior smaller-scale one to investigate the interactions between topography, rotation and buoyancy in the turbulent regime (which cannot be tackled with theory or numerics). Simultaneously, combining symbolic and arbitrary precision numeric computations, the PhD student R. Monville has developed from scratch an innovative code to provide accurate estimates of the topography driven stress generated by core (or laboratory experiment) flows on a rigid domain (e.g. an electrically conducting lowermost layer of the mantle), including the effects of rotation, buoyancy, viscosity and magnetic fields (Monville et al., in prep). Such a code will allow us to bridge the gap between laboratory experiments, oceanic or atmospheric studies, and planetary liquid cores.
• WP3 (Magnetic field effects): we have obtained and validated the first (kinematic) dynamo magnetic fields in tidally-deformed spheres (Vidal & Cébron, Proc. R. Soc. A 2021), that is for large-scale departure from the spherical geometry. While the Early Moon paleofield data motivates our study of precession driven dynamos, we have shown that the most relevant forcing for the Early Earth paleodynamo is actually the tidal one (Landeau et al., Nat Rev Earth Environ 2023), motivating our on-going dedicated study.
These models and results have been communicated in various international conferences (e.g. IAGA 2021, SEDI 2022, AGU 2022, etc.).
• WP1 (topography driven flows): we have obtained the mean zonal core flows due to orbital forcings (precession, tides, etc.) in deformed spherical shells (Cébron et al., J. Fluid Mech. 2021). Using a new mathematical formulation, the eigenmodes of a tidally-deformed planetary core have also been obtained, including density and pressure variations (Vidal & Cébron, Proc. R. Soc. A, 2020). Extending this new method, we have proposed a new approach to unlock the simulations of core turbulence due to orbital forcings in non-spherical geometries (which were hampered by viscous layers, see Vidal & Cébron, J. Fluid Mech. 2023).
• WP2 (interaction with buoyancy): we are currently developing a large-scale experiment, as well as a prior smaller-scale one to investigate the interactions between topography, rotation and buoyancy in the turbulent regime (which cannot be tackled with theory or numerics). Simultaneously, combining symbolic and arbitrary precision numeric computations, the PhD student R. Monville has developed from scratch an innovative code to provide accurate estimates of the topography driven stress generated by core (or laboratory experiment) flows on a rigid domain (e.g. an electrically conducting lowermost layer of the mantle), including the effects of rotation, buoyancy, viscosity and magnetic fields (Monville et al., in prep). Such a code will allow us to bridge the gap between laboratory experiments, oceanic or atmospheric studies, and planetary liquid cores.
• WP3 (Magnetic field effects): we have obtained and validated the first (kinematic) dynamo magnetic fields in tidally-deformed spheres (Vidal & Cébron, Proc. R. Soc. A 2021), that is for large-scale departure from the spherical geometry. While the Early Moon paleofield data motivates our study of precession driven dynamos, we have shown that the most relevant forcing for the Early Earth paleodynamo is actually the tidal one (Landeau et al., Nat Rev Earth Environ 2023), motivating our on-going dedicated study.
These models and results have been communicated in various international conferences (e.g. IAGA 2021, SEDI 2022, AGU 2022, etc.).
We have been working in parallel on the three scientific tasks of the project. The first scientific steps have been successfully validated through analytical and numerical results, which have been obtained thanks to new mathematical and numerical developments. We will pursue this way during the next period, with a focus on:
• WP 1: mathematical development and numerical implementation of an asymptotic parametrization of the leading-order viscous effects in our bespoke Galerkin spectral code for tidally-deformed ellipsoidal cores. This approach is key to avoid resolving the smallest length scales of the flow dynamics, which are only of secondary importance for the dynamics. This will allow us to truncate our reduced models to obtain an enhanced efficiency of our numerical code.
• WP 2: building the two experimental setups, which are key to explore the turbulent regimes (inaccessible to numerical simulations).
• WP 3: modifying a very fast spectral dynamo code to handle consistently weak boundary departures from the spherical geometry.
Our research on small-sale topographic effects will also be published, revising the role of the topography in the measurements of nutations and length of the day.
• WP 1: mathematical development and numerical implementation of an asymptotic parametrization of the leading-order viscous effects in our bespoke Galerkin spectral code for tidally-deformed ellipsoidal cores. This approach is key to avoid resolving the smallest length scales of the flow dynamics, which are only of secondary importance for the dynamics. This will allow us to truncate our reduced models to obtain an enhanced efficiency of our numerical code.
• WP 2: building the two experimental setups, which are key to explore the turbulent regimes (inaccessible to numerical simulations).
• WP 3: modifying a very fast spectral dynamo code to handle consistently weak boundary departures from the spherical geometry.
Our research on small-sale topographic effects will also be published, revising the role of the topography in the measurements of nutations and length of the day.