ISTerre - Institut des Sciences de la Terre

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?

current post-doc proposals

2020-03-12T15:21:35Z

- Internships, PhD, post-doc offers

Zonal winds

Dominique JAULT, Henri-Claude NATAF, Philippe CARDIN — 2019-10-15T13:36:40Z

Zonal winds are axisymmetric flows in rotating geophysical systems such as atmopheres, oceans or cores. We'd like to understand the physical mechanism responsible of their presence, their amplitude and their geometry.
The zonal flows are east-west wind (along lines parallel to the equator of a sphere) which turns around the axis of rotation of the planet. An image of Jupiter gives us a clear representation of what they are.

NASA

Jupiter observed by Voyager, NASA

We mainly focus in deep layer systems where the rotation (through the Coriolis forces) imposes a geometrical constraint on the flow, known as geostrophic constraint. The zonal flows are quite peculiar because they cannot originate from radial forcing such as boyancy forces but are produced by non linear interaction of the flow in presence of rotation. Result of rotating turbulence, these flows are difficult to compute.

Equatorial view of the longitudinal velocities (in Reynolds number) in rapidly rotating convection showing multiple azimuthal jets. from Guervilly et al (GJI 2017)

In ISTerre, we built an experimental set up, called ZoRo (for Zonal flows in Rotating fluids), to study zonal flows. We study the flow of aire embedded inside a rotating spheroidal cavity (up to 30Hz). In order to measure the flow, we develop a velocimetry method based on pertubations of acoustic modes.

Photograp of the experimental setup - Max Solazzo

Quasigeostrophy

Dominique JAULT, Henri-Claude NATAF, Nicolas GILLET, Philippe CARDIN — 2019-10-15T13:22:06Z

We expect Earth rotation to make the motions in the core columnar, nearly invariant in the direction parallel to the rotation axis. Geodynamo simulations nicely reproduce this feature.

Assuming columnar geometry (quasi-geostrophic hypothesis), we find that the motions depend only on the spatial coordinates in a plane perpendicular to the rotation axis, making the problem two-dimensional and reducing its size significantly.

There is a large body of research on quasi-geostrophic flows that has been developed specifically to better understand motions in thin fluid layers (Earth atmosphere and oceans). We use this approximation to compute dynamical regimes of thermal convection instead in a rapidly rotating sphere.
We have been able to reproduce turbulent convection for very low viscosity and to exhibit a regime where the small diffusivities do not control the dynamics. Interestingly, in this new regime, we discover that thermal convection becomes subcritical and consequently shuts down abruptly, which could explain rapid extinction of some ancient planetary dynamos (Mars, Moon…).

We have also obtained a new set of reduced quasi-geostrophic momentum equations valid in deep shells, such as planetary cores, including their equatorial regions. We generalize these equations to non spherical bodies in order to document the pressure coupling between the fluid and its solid boundaries. We thus obtain very good approximations of the slowest inertial modes. We are also pairing the quasi-geostrophic equation with the induction equation (for the magnetic field) in order to model the secular variation of the Earth's magnetic field.

Deep Earth

Dominique JAULT, Henri-Claude NATAF, Philippe CARDIN, Renaud DEGUEN — 2019-10-10T09:25:50Z

One of the main objective of the group is to understand the dynamics and evolution of the deep interior of Earth and terrestrial planets. We use for this a combination of theoretical and numerical modelling, fluid dynamics experiments, and high pressure mineral physics experiments.

Topics currently under investigation include:
– the generation of magnetic field in planetary cores through dynamo effect
– accretion and core/mantle differentiation of terrestrial planets
– physical properties of the mantle and core of terrestrial planets (including exoplanets)
– convection in a crystallizing mantle and magma oceans
– Earth's inner core crystallisation and dynamics
– ...

Mineral Physics

Terrestrial planets are constituted of different layers, mainly a silicate mantle surrounding a metallic core. With increasing depth, pressure and temperature increase, modifying the physical properties of the materials, such as density, crystallographic structure, etc … These changes strongly affect the dynamic of the whole planet. To constrain the actual state of a planet, as well as its evolution from its early stage, it is mandatory to perform measurements on materials under planetary interiors conditions. Mineral Physics approach aim at using different experimental tools, such as Diamond Anvil Cell, Multi-Anvil press or Laser-driven Shock Compression, to unravel density, structure, phase diagram or transport properties of geomaterials under extreme conditions. The explored conditions will span from few GPa, for the Moon's interior, to several hundreds of GPa for large exoplanets.

Accretion and core/mantle differentiation of terrestrial planets

Geomagnetic data analysis

Dominique JAULT, Henri-Claude NATAF, Nicolas GILLET, Philippe CARDIN — 2019-09-14T13:37:05Z

The Swarm mission of ESA is today central to the efforts carried by the geomagnetic community. It will allow a better description of external magnetic fields, and thus open a window towards the dynamics in the core at interannual (to monthly ?) periods. This evolution occurs at the same time a new generation of geodynamo simulations arises. It is timely to combine the above two aspects through data assimilation studies. Because we only have access to a limited amount of geophysical constraints (the field at the core surface), this requires to develop reduced models able to reproduce the rapid dynamics in the core. This is the rationale under the development of magnetic quasi-geostrophic equations, or of stochastic models anchored to geodynamo statistics.

Our efforts are supported by the Centre National d'Etudes Spatiales (CNES). In this context, we propose several products to the community:

– the geomagnetic data assimilation tool pygeodyn;

– the web platform webgeodyn for core surface flow and magnetic field visualization;

– the magnetic field model COV-OBS that covers eras of observatory and satellites magnetic records (1840-2020, coll. DTU Space, Copenhagen).

Vulgarisation

Philippe CARDIN — 2019-08-29T07:25:06Z

VULGARISATION
– Pourquoi faire des expériences ?

Experiences Géodynamo

– Présentation des métiers de la recherche

Les métiers de la recherche

– Voir la sphère DTS (expérience sodium) en PDF 3D

Sphère DTS 3D

– Pour la visite virtuelle de DTS : cliquer sur l'image
img4162

VIDEOS
– "La Terre, cet aimant géant" France 5
https://www.youtube.com/watch?v=lpQd25uWSKw
– "Voyage au centre de la Terre" CNRS
http://videotheque.cnrs.fr/video.php?urlaction=visualisation&method=QT&action=visu&id=1102&type=grandPublic

MEDIAS
– Mécanique des Fluides
Enseignement à Ense3 : réalisation de banc didactique

Ense3 Banc didactique Débit Visu

Presentation de la Geodynamo pour tout public

Philippe CARDIN — 2019-08-29T07:24:27Z

Sphère DTS 3D

Experiences Géodynamo

Quelques éléments de métrologie

Présentation grand public de la géodynamo

Former team members

Henri-Claude NATAF, Nicolas GILLET, Philippe CARDIN — 2019-08-26T15:31:29Z

– Guillaume Morard (Chargé de Recherche CNRS 2019-2023) is now in Institut de minéralogie, de physique des matériaux et de cosmochimie in Paris.
Guillaume Morard sur ResearchGate

– Mathieu Istas (Ingénieur de Recherche CNRS, CDD CNES 2020-2023). Membre du Service Geodata d'ISTerre. En charge du développement des outils pygeodyn et webgeodyn. Maintenant Ingénieur de Recherche CNRS à l'Institut Néel.
Mathieu Istas sur Linkedin

– Loïc Huder (Ingénieur d'Etudes CNRS, CDD CNES 2018-2020). Membre du Service Geodata d'ISTerre. En charge du développement des outils pygeodyn et webgeodyn. Maintenant Ingénieur à l'ESRF.
Loïc Huder sur GitHub

– Adeline Richard (Ingénieure d'Etudes CNRS 2008-2017) à mi-temps dans l'équipe géodynamo. Maintenant affectée au Laboratoire de Physique Subatomique et Cosmologie.

– Patrick La Rizza (Ingénieur d'Etude CNRS 2006-2016). Ingénieur électronicien. Retraité.

– Jean-Paul Masson (Ingénieur de Recherche CNRS 1999-2016). Ingénieur mécanicien. Cristal du CNRS en 2005. Retraité.
Quelques archives de J-P. Masson

– Denys Schmitt (directeur de recherche CNRS, 2005-2012). Retraité en octobre 2012, puis décédé en août 2015. Liste de publications et journée scientifique organisée en son hommage.

– Thierry Alboussière (2003 - 2009) Checheur CNRS dans l'équipe. Actuellement directeur de recherche au laboratoire de Géologie de Lyon.

– Alexandre Fournier (2004-2008) maitre de conférence à l'université Joseph Fourier et chercheur dans l'équipe. Actuellement professeur à l'Institut de Physique du Globe de Paris.

– Daniel Brito, (1998-2008) maitre de conférence à l'université Joseph Fourier et chercheur dans l'équipe. Actuellement, professeur à l'université de Pau.

Former post-docs

Henri-Claude NATAF, Nicolas GILLET, Philippe CARDIN — 2019-08-26T15:31:18Z

– Hannah Rogers

– Kang Wei Lim

– Ludovic Huguet

– Tobias Schwaiger (postdoc CNES xx-2022)

– Manohar Kumar Sharma

– Long Chen

– Jenny Wong (postdoc 2019-2021) : dans le cadre du projet ERC SEIC (Setting Earth's Initial Conditions) de Renaud Deguen.

– Elliot Kaplan (postdoc CNRS 2015-2016) : simulations numériques DTS et convection, dans le cadre de l'ANR TuDy.

– Aldo Figueroa (postdoc CNRS en 2011-2012), Modes and instabilities in magnetized spherical Couette flow, enseignant chercheur au Mexique.

– Céline Eymin

– Douglas Mac Lean