ISTerre - Institut des Sciences de la Terre

ERC project THEIA

David CÉBRON, Jérémie VIDAL, Max SOLAZZO — 2022-02-14T07:38:21Z

Why building experiments?

In the frame of the ERC project THEIA, we aim at combining theory, numerics and experiments. They are indeed complementary to investigate the coupling between a solid boundary and a fluid flow, such as the one at the seafloor or at the Core-Mantle Boundary (CMB) :

Theory gives physical insights and can directly probe the relevant regime of weak diffusivities and large magnetic fields. But it remains limited to laminar or weak turbulence, and dynamo studies remain a challenge.
Numerics can handle spherical-like geometries, with all the physical ingredients, giving the flow in the whole volume. But it is limited to laminar or weak turbulence, and diffusive effects are over-estimated. Moreover, it remains challenging to include topographic effects in simulations.
Experiments can easily probe the turbulent regime, a key ingredient which remains intractable with theory or numerics. It can also tackle any kind of topography. But the weakly diffusive magnetic effects or the spherical-like geometry remain out-of-reach.

Two experiments

To investigate turbulent boundary couplings in presence of rotation, density variations and topography, we are developing an experimental setup at two different scales: a small, but versatile and easy to modify, setup called mini-THEIA, and a large-scale experiment, less flexible but capable of probing other regimes (e.g. waves interactions):

Mini-THEIA will be able to tackle various experiments in rotating flows. It will allow a continuous filling and draining of the experimental tank, while in rotation (notably to avoid the mixing due to the fluid spin-up). Typical planned experiments are

Linear spin-up (or spin-down) of a stratified fluid in presence of topography, in the continuity of Burmann & Noir (2018).
Coupling of floating bodies (in order to get rid off unwanted solid friction)
Filling box experiments, with plume injections and draining while in rotation (collaboration with Prof. Renaud Deguen)
Slichter modes measurements, with a rotating flow
Libration Driven square instabilities (LDSI) will be excited and compared with theory (collaboration with Jérémie Vidal)

The large-scale experiment THEIA requires severe modifications of the experimental room to host the rotating 18T experiment of salty water. This long-term goal experiment will allow to study the boundary wave drag when rotation, topography and turbulence are simultaneously present. It is still under development, and mini-THEIA will help to design it.

ERC project THEIA

David CÉBRON, Jérémie VIDAL, Max SOLAZZO — 2022-02-10T09:07:26Z

In the frame of the ERC project THEIA, we develop from scratch new codes (e.g. ToCCo), or we modify existing efficient codes (e.g. XSHELLS) to investigate small and large scale topographic effects. We detail below some of the codes currently developed and used in the project:

1. ToCCo (Topographic Coupling at Core-Mantle interface), developed by R. Monville, combines symbolic and arbitrary-precision numerical calculations in a local Cartesian box in order to calculate the Boussinesq magneto-hydrodynamic laminar flow along one or two (possibly conducting) solid domains, forced by rotation, topographic, buoyancy and magnetic effects (providing the total boundary stress from pressure, viscous and electromagnetic forces).
Associated ERC project publications: Monville, Cébron, Jault (2022, in prep.)

2. SHINE (Solver for Hydromagnetic INviscid modes in Ellipsoids), developed by J. Vidal computes the diffusionless hydromagnetic eigenmodes of either Boussinesq or fully compressible fluids enclosed in co-rotating triaxial ellipsoids. The code handles polynomial perturbations of unprecedented spatial complexity.
Associated ERC project publications: Vidal & Cébron (2020, PRSA), Vidal & Cébron (2021, JASA), Vidal & Cébron (2021, PRSA)

3. SWAN (Short-Wavelength stability ANalysis), developed by J. Vidal, probes the linear hydromagnetic stability of generic Boussinesq basic states, by considering short-wavelength perturbations (Lifschitz & Hameiri, 1991). This code gives sufficient conditions for local diffusionless instability.
Associated ERC project publications: Vidal & Cébron (2022, in prep.)

4. SIREN (Stability with IneRtial eigENmodes), developed by J. Vidal, probes the linear stability of arbitrary basic flows of uniform vorticity, forced by orbital forcings and enclosed within rigid ellipsoids. The code handles polynomial perturbations of unprecedented spatial complexity in the ellipsoid.
Associated ERC project publications: Vidal & Cébron (2022, in prep.)

5. XSHELLS, developed by N. Schaeffer, performs spectral direct numerical simulations (DNS) in spherical geometries using sphericl harmonics.
Associated ERC project publications: Cébron et al. (2021)

ERC project THEIA

David CÉBRON, Jérémie VIDAL, Max SOLAZZO — 2022-02-10T09:01:26Z

- 2025 -

27. Personnettaz P., Meresse A., Cébron D., Schaëffer N., Laminar to turbulent transition in librating spheres
2nd European Fluid Dynamics Conference (EFDC2), Dublin (Ireland), 26-29 August 2025.

26. Cébron D. , Unravelling the dynamics of non-spherical planetary cores
Thème Intérieurs de la Terre et des planètes. Invited seminar at IPG Paris, France, April 03, 2025.

- 2024 -

25. Personnettaz P., Schaëffer N., Cébron D., Mandea M., Fluid response to the inner core's translational oscillations
Rencontres du Non-Linéaire, Paris, March 19-20, 2024.

24. Monville R., Cébron D. & Jault D. , Topographic effects in planetary magneto-hydrodynamic ﬂows
Rencontres du Non-Linéaire, Paris, March 19-20, 2024. PDF

23. Vidal J. , Inertia-gravity waves in geophysical vortices
Seminar, Institut de Mathématiques de Bourgogne, Université de Bourgogne (France), February 20, 2024. PDF

22. Vidal J. , Ondes d'inertie-gravité dans un fluide confiné, applications géophysiques
Seminar "MathsInFluids" - UMPA, ENS Lyon (France), February 2, 2024. PDF

21. Personnettaz P., Monville R., Schaëffer N., Cébron D., Mandea M., Beyond spherical boundaries in deep fluid layers of planets
1st European Fluid Dynamics Conference (EFDC1), Aachen (Germany), September 16-20, 2024.

- 2023 -

20. Vidal J. , Inertia-gravity waves in geophysical vortices
"Spectral and Resonance Problems for Imaging, Seismology and Materials Science", Université de Reims Champagne-Ardenne (France), November 20-24, 2023. PDF

19. Cébron D. , Simulations of non-spherical liquid cores of planets
Beyond Boussinesq for Astrophysical and Geophysical fluids: Numerical tools and experiments of the future. ENS Lyon, France, October 19, 2023.

18. Personnettaz P., Cébron D., Schaëffer N., Mandea M., Dissipation mechanisms of the inner core's translational oscillations
Journées CNES (JC2) 2023, Toulouse (France), October 11-13, 2023.

17. Personnettaz P., Cébron D., Schaëffer N., Mandea M., Modeling non-spherical eﬀects with parametrized boundary conditions
GAFDEM: Geophysical Astrophysical Fluid Dynamics: Experiments and models, Nice (France), September 11-15, 2023.

16. Monville R., Vidal J., Cébron D. & Schaeffer N., Topographic coupling at the core mantle boundary
28th General Assembly of The IUGG, Berlin (Germany), July 11-20 2023. PDF

15. Monville R., Vidal J., Cébron D. & Schaeffer N., Generation of planetary core zonal flows by orbital forcings or fingering convection
28th General Assembly of The IUGG, Berlin (Germany), July 11-20 2023. PDF

14. Cébron D., Monville R., Vidal J., Sauret A. & Schaeffer N., Generation of planetary core zonal flows by orbital forcings or fingering convection
28th General Assembly of The IUGG, Berlin (Germany), July 11-20 2023. PDF

13. Vidal J. & Cébron D., Precession-driven flows and turbulence in planetary liquid cores
28th General Assembly of The IUGG, Berlin (Germany), July 11-20 2023. PDF

12. Vidal J. & Cébron D., Asymptotic models of rotating flows in stress-free ellipsoids
26eme Rencontre du Non Linéaire, Paris (France), March 28-30 2023. PDF

- 2022 -

11. Monville R., Cébron D., Schaeffer N., Topographic Effects in Magnetized and Stratified Fluid Cores
AGU Fall Meeting, Chicago (USA), December 12-16 2022.

10. Monville R., Vidal J., Cébron D., Schaeffer N., Rotating Double-Diffusive Convection: Flows and Dynamos in Stably Stratified Deep Layers of Planets
AGU Fall Meeting, Chicago (USA), December 12-16 2022. PDF

9. Monville R., Cébron D., Jault D., Topographic effects in magnetized and stratified fluid cores,
17th Symposium of SEDI, ETH Zurich (Switzerland), July 11- July 15 2022.

8. Cébron D., Monville R., Vidal J., Sauret A., Schaeffer N., Generation of planetary core zonal flows by mechanical forcings & fingering convection
17th Symposium of SEDI, ETH Zurich (Switzerland), July 11- July 15 2022.

7. Vidal J., Cébron D., Asymptotic models of rotating flows in ellipsoidal planets
17th Symposium of SEDI, ETH Zurich (Switzerland), July 11- July 15 2022.

6. Monville R., Cébron D., Jault D., Topographic effects in magnetized and stratified fluid cores
17th Colloque quadriennal de bilan et prospective du PNP, ENS Lyon (France), June 29- July 1 2022

5. Cébron D., Monville R., Vidal J., Sauret A., Schaeffer N., Generation of planetary core zonal flows by mechanical forcings & fingering convection
Colloque quadriennal de bilan et prospective du PNP, ENS Lyon (France), June 29- July 1 2022.

4. Vidal J. & Cébron D., Asymptotic models of rotating flows in ellipsoidal planets
Colloque quadriennal de bilan et prospective du PNP, ENS Lyon (France), June 29- July 1 2022.

- 2021 -

3. Monville R., Cébron D., Jault D., Topographic effects in a stratified layer at the top of the Earth's core
Workshop Grenoble-Zurich-Marseille-ROB, ETH Zurich (Switzerland), November 16 2021.

2. Vidal J. & Cébron D., Kinematic dynamos in triaxial ellipsoids
Workshop Grenoble-Zurich-Marseille-ROB, ETH Zurich (Switzerland), November 16 2021.

1. Monville R., Cébron D., Jault D., Topographic effects at the core-mantle boundary
International conference IAGA-IASPEI 2021, Hyderabad (India), 21-27 August 2021.

ERC project THEIA

David CÉBRON, Jérémie VIDAL, Max SOLAZZO — 2022-02-09T07:48:38Z

- 2025 -

22. Semiconvection in rotating spherical shells
P. Pruzina, D. Cébron , N. Schaeffer, J. Vidal,
In prep.

21. Investigating the Drag Force Due to Inertial Waves Generated by Topography
V. Giraud, J. Noir, R. Monville, J. Vidal, D. Cébron ,
In prep.

20. Hydromagnetic drag on a rapidly oscillating sphere
D. Cébron & P. Personnettaz,
In prep.

19. Dissipation of the translational oscillations of the inner core
P. Personnettaz, D. Cébron, N. Schaeffer, R. Deguen, M. Mandea,
In prep.

18. Did lunar tides sustain the early Earth's geodynamo?
J. Vidal & D. Cébron
In review. PDF

17. Semiconvection unlocks dynamo action in stably-stratified regions of gaseous planets
P. Pruzina, D. Cébron , N. Schaeffer,
In review. PDF

16. Modal Acoustic Velocimetry in libration-driven flows
H.-C. Nataf, S. Su, P. Roux, P. Cardin, D. Cébron, Y. Do,
In review.

15. On gravito-inertial surface waves
Y. Colin de Verdière & J. Vidal
Contemporary Mathematics (accepted). Preprint

14. The spectrum of the Poincaré operator in an ellipsoid
Y. Colin de Verdière & J. Vidal
Journal of Spectral Theory. Preprint

13. Topographic Drag at the Core-Mantle Interface
R. Monville, D. Cébron, D. Jault,
Journal of Geophysical Research - Solid Earth, 130, e2024JB029770, 2025. PDF, Supp. Mat.

- 2024 -

12. Inertia-gravity waves in geophysical vortices
Vidal J. & Colin de Verdière Y., 2024,
Proceeding of the Royal Society A, 480 (2285), 20230789. PDF

11. Geophysical flows with topography, a playground for laboratory experiments
J. Vidal, J. Noir, D. Cébron, F. Burmann, R. Monville, V. Giraud,
Comptes Rendus. Physique, pp. 1-52, 2024. PDF

10. Compaction-driven convection in the growing inner core
K. W. Lim, R. Deguen, D. Cébron, A. Schulze, M. Mandea,
Geophysical Research Letters, 51, e2024GL110749, 2024. PDF, Sup. Mat.

- 2023 -

9. MHz free electron laser x-ray diffraction and modeling of pulsed laser heated diamond anvil cell
N. Jaisle, D. Cébron, Z. Konôpková, et al.,
Journal of Applied Physics, 134, 095904, 2023. PDF

8. Precession-driven flows in stress-free ellipsoids
J. Vidal & D. Cébron
Journal of Fluid Mechanics, 954, A5, 2023. PDF

- 2022 -

7. Sustaining Earth's magnetic dynamo
M. Landeau, A. Fournier, H.-C. Nataf, D. Cébron, N. Schaeffer
Nature Reviews Earth & Environment, 3, 255–269, 2022. PDF, or open link

6. Core Eigenmodes and their Impact on the Earth's Rotation
S. A. Triana, M. Dumberry, D. Cébron, J. Vidal, A. Trinh., F. Gerick, J. Rekier,
Surveys in Geophysics, 43, 107-148, 2022. PDF

- 2021 -

5. Acoustic modes of rapidly rotating ellipsoids subject to centrifugal gravity
J. Vidal & D. Cébron,
Journal of the Acoustical Society of America, 150 (2), 1467-1478, 2021. PDF

4. The effects of a Robin boundary condition on thermal convection in a rotating spherical shell
T. Clarte, N. Schaeffer, S. Labrosse & J. Vidal,
Journal of Fluid Mechanics, 918, A36, 2021. PDF

3. Kinematic dynamos in triaxial ellipsoids
J. Vidal & D. Cébron,
Proceedings of the Royal Society A, 477 (2252), 20210252, 2021. PDF

2. Mean zonal flows induced by weak mechanical forcings in rotating spheroids
D. Cébron, J. Vidal, N. Schaeffer, A. Borderies, A. Sauret,
Journal of Fluid Mechanics, 916, A39, 2021. PDF

- 2020 -

1. Acoustic and inertial modes in planetary-like rotating ellipsoids
J. Vidal & D. Cébron,
Proceedings of the Royal Society A, 476, 20200131, 2020. PDF

ERC project THEIA

David CÉBRON, Jérémie VIDAL, Max SOLAZZO — 2022-02-09T07:47:35Z

- Current members -

PI : David Cébron, CNRS researcher and team leader of the Geodynamo group of ISTerre

Research Fellow (2024-2025) : Paul Pruzina, working on semi-convection dynamo in planetary spherical fluid layers in rapid rotation

Research Fellow (2025-2026) : Paolo Personnettaz, working on parameterization of topographic effects in spherical planetary cores

Engineer : Max Solazzo, CNRS engineer (ISTerre), who design and build the planned project experiments (turbulence studies)

ISTerre collaborators : the Geodynamo group, in particular D. Jault for theory, N. Schaeffer for the XSHELLS simulations, R. Deguen and H.-C. Nataf for the experiments

- Past members -

PhD (2020-2024) : Rémy Monville, working on small scale topographic effects (local models). Phd topic: Topographic coupling in planetary cores

Research Fellow (2020-2025) : Jérémie Vidal, working on ellipsoidal planetary cores (global models) to study large scale topographic effects

The ZoRo experiment

David CÉBRON, Henri-Claude NATAF, Max SOLAZZO, Philippe CARDIN, Yann DO — 2020-07-06T10:17:29Z

Funded by the French National Research Agency (ANR) through the TuDy project (2013-2019), the ZoRo experiment was built to investigate the formation of zonal jets in rotating fluids, such as the atmospheres of giant planets (Jupiter, Saturn), and planetary liquid cores. The ZoRo project was further funded by Labex OSUG@2020 (2013-2014) and Programme National de Planétologie (2022).

The geodynamo team has developed a unique method to map fluid flow in a rapidly rotating gas-filled spheroid: the Modal Acoustic Velocimetry (Triana et al, 2014; Su et al, 2020; Vidal et al., 2020; Nataf et al, 2025).

Have a look at the very clear presentation of the ZoRobot project by intern Gregory de Salaberry Seljak (2022)!

Zonal jets

Jupiter and aurora

Hubble Space Telescope • WFC3/UVIS • STIS
credits: NASA, ESA, and J. Nichols (University of Leicester)

NASA, ESA, and J. Nichols (University of Leicester)

Strong alternating eastwards and westwards jets shape the surface of Jupiter and Saturn. They are fueled by convective motions in their atmospheres, which are converted into strong zonal jets under the action of the Coriolis force.

What controls the number of jets and their velocities? This is not well understood yet. Numerical simulations reproduce such features, but planetary regimes remain out of reach.

Quasi-geostrophic numerical simulation of convective jets

View from the pole of convective zonal jets in a sphere. E=10^-8, Pr=0.1, Ra=9 Ra_c.
credits: Céline Guervilly

Céline Guervilly

The ZoRo set-up

The ZoRo experiment at ISTerre

credits: M. Solazzo

M. Solazzo

We built the ZoRo experiment to investigate the formation of convective zonal jets in a rapidly rotating gas-filled spheroid (a sphere flattened at the poles). The inner equatorial radius of the spheroid is r_eq=20 cm, while its polar radius is r_pol=19 cm. We can rotate ZoRo up to 50 rotation per seconds. The spheroid can be filled with various gases in order to change the fluid flow parameters.

Fluid flow is measured by an acoustic method. We use 4 small loudspeakers to produce sounds, which are recorded by 14 tiny microphones. All the electric signals pass from the rotating spheroid to the Lab through slip-rings.

The spheroidal cavity has been machined with great precision. Special care has been taken to limit the noise produced by the rotation of ZoRo. All instrumentation respect symmetries about the axis of rotation and about the equator, in order to insure a balance down to a gram level (see Su et al, 2020, technical drawings for more details).

Acoustic modes in a sphere

Just like sounds of various frequencies can be generated in a pipe or a flute, a gas-filled sphere can resonate at various frequencies. Resonances occur at specific frequencies, which are produced by specific vibration patterns, called acoustic modes.

In a sphere, the surface pattern of modes is given by spherical harmonics Y_l^m(theta,phi), while their radial dependency involves spherical Bessel functions j_l(k_nl r). The triplet of integer mode numbers (n,l,m) defines an acoustic mode. Mode numbers give the number of zero crossing of the vibration pattern: in radius for n, at the surface for l, and in azimuth phi for m. Following seismological conventions, we label modes as _nS_l^m.

In a perfect sphere, the frequency of _nS_l^m modes does not depend upon m: modes are degenerate.

Pattern of spherical harmonics Y_l^m

From top to bottom, mode number l increases from 0 to 4. Azimuthal mode number m increases from -l to +l from left to right. The central column corresponds to axisymmetric acoustic modes (m=0).

credits: Florian T. Pokorny, KTH Royal Institute of Technology.

Florian T. Pokorny, KTH Royal Institute of Technology

Modal Acoustic Velocimetry

Modal Acoustic Velocimetry is a new experimental technique introduced by Triana et al, 2014. It relies on the Doppler effect.

Acoustic modes can be regarded as resulting from the constructive interference of waves travelling in opposite directions. For instance, modes _nS_l^+m and _nS_l^-m result from the interference of waves traveling in the prograde and retrograde azimuthal directions. These two waves will experience an opposite Doppler effect when an azimuthal flow is present. This lifts the ±m-degeneracy: the _nS_l^±m doublet will split into two peaks at distinct frequencies. More surprisingly, the simple rotation of the fluid and its container can produce a splitting, under the effect of the Coriolis force, even in the absence of differential flow.

A similar method has been used by helioseismologists to unravel azimuthal flows within the Sun!

Exciting and recording acoustic modes

An example of linear chirp

credit: Georg-Johann / CC BY-SA

Georg-Johann / CC BY-SA

Acoustic modes are excited successively by letting ZoRo's loudspeakers play a linear chirp from 500 to 5000 Hz.

Check by yourself what the chirp sounds like!

Microphones record the response of ZoRo to this excitation. The frequency spectrum of these records reveals the resonance peaks of the acoustic modes.

45s-long linear chirp from 500 to 5000 Hz

credits: Ph. Cardin.

The music of ZoRo

Part of the acoustic spectrum of ZoRo at rest

f0 = 0 Hz : recorded spectrum from 1200 to 2200 Hz. The vertical lines mark the frequencies of the expected resonances of acoustic modes. The names of the nSl multiplets are indicated.

Because ZoRo is a spheroid rather than a sphere, the m-degeneracy of the acoustic modes is partly lifted: the resonance frequency of an _nS_l^±m doublet depends on |m| (colored vertical bars give their predicted frequencies).

part of the acoustic record of ZoRo at rest

H-C. Nataf

Exercise your ear: try to identify all the resonances displayed in the spectrum.

Part of the acoustic spectrum of ZoRo spinning at 15 rotations per second

f0 = 15 Hz : recorded spectrum from 1200 to 2200 Hz. The vertical lines mark the frequencies of the expected resonances of acoustic modes. The names of the nSl multiplets are indicated.

When ZoRo is spinning, acoustic modes are split under the action of the Coriolis force. Now the _nS_l^-m and _nS_l^+m singlets show up at slightly different frequencies (pairs of colored vertical bars indicate their expected splitting). The same is observed for the seismic modes of the Earth!

part of the acoustic record of ZoRo spinning at 15 rotations per second

H-C. Nataf

Exercise your ear: can you hear the small differences from the record at rest?