ISTerre - Institut des Sciences de la Terre

LabEx OSUG@2020 - Vélocimétrie par splitting de modes acoustiques

Henri-Claude NATAF — 2025-09-05T14:40:14Z

We develop a new method to infer fluid flow inside a spherical shell from the splitting of its acoustic modes.

Durée : 2013 - 2014

Financement : LabEx OSUG@2020

Coordinateur : Henri-Claude Nataf (ISTerre)

Equipes ISTerre impliquées :
– Géodynamo
– Ondes et Structures

Collaborations :
– University of Maryland - Dan Lathrop's Non Linear Lab

Les héliosismologues cartographient le champ de vitesse à l'intérieur du Soleil en inversant le ‘splitting' de ses modes normaux acoustiques. Peut-on appliquer une technique similaire pour cartographier les grandes échelles de l'écoulement dans des expériences de Laboratoire ?

Profitant des expertises complémentaires des équipes “géodynamo” et “ondes et structures” d'ISTerre, nous testons cette possibilité à l'aide d'expériences modèles très simples. On cherche en particulier à examiner l'apport d'un réseau d'accéléromètres dans l'identification des modes.

En cas de succès, la méthode sera appliquée à l'expérience DTS en sodium liquide, puis à d'autres expériences. Le gros avantage d'une telle technique est qu'elle ne repose pas sur la présence de diffuseurs en suspension dans le liquide. Elle est particulièrement adaptée aux expériences dans une sphère en rotation rapide.

TuDy : Turbulence et Dynamo dans les noyaux planétaires

David CÉBRON, Henri-Claude NATAF — 2025-09-05T13:50:18Z

- Projets terminés

Catalogue of planetary dynamo simulations

Henri-Claude NATAF, Romain Claveau — 2025-06-10T13:24:45Z

A joint effort to catalogue the available Planetary dynamo simulations

Screen shot of an output of the catalogue

Grand prix Ampère de l'Electricité de France awarded to the geodynamo team!

Henri-Claude NATAF — 2021-11-24T08:19:23Z

On 23 November, took place under the dome of the Institut de France, the Award ceremony of the Academy of Sciences 2021. These awards honour experienced scientists or young researchers at the beginning of their careers. Through them, the Academy of Sciences contributes directly to its mission of encouraging scientific life.

Among these awards, the Prix Ampère de l'Électricité de France 2021 was awarded to the Géodynamo team of ISTerre. This award recognises one or more researchers working in a French laboratory for outstanding research work in the field of mathematical or physical sciences, fundamental or applied.

Created in 1997, the Geodynamo team explores the dynamics of the Earth's core and the origin of planetary magnetic fields. Its work has shed light on the major role of rotation on the quasi-geostrophic organisation of flows in the core, and has led to the discovery of geostrophic Alfvén waves in the core. Its studies were always guided by experimental results. In particular, the team's flagship experiment (DTS, using liquid sodium) was distinguished by its very advanced instrumentation (velocimetry, magnetometry). The interpretation of the geomagnetic observations was also based on the geodynamic simulations carried out by the team, which reached extreme spatial and temporal resolutions thanks to a new spherical harmonic transformation algorithm.

The Academy paid tribute to the geodynamo team at the award ceremony under the dome of the Institut de France on 23 November 2021. The team would like to associate its collaborators and former members to this honour.

Review the ceremony on Youtube (Presentation of the Ampère Prize at 25:53)

Geomagnetic data

Henri-Claude NATAF — 2020-11-02T10:51:34Z

Movie of the time-evolution (from 1840 to 2020) of Br at the surface of the Earth's core, built from COV-OBS.x1 model (Gillet et al, 2015), using the webgeodyn platform. Aitoff map projection.

Time-evolution of the magnetic field at the CMB

Archeomagnetism: movie of the time-evolution (from 1200BC to 2020AD) of Br at the surface of the Earth's core, built from COV-ARCH model (Hellio and Gillet, 2018), using the webgeodyn platform. Aitoff map projection.

Archeomagnetism: magnetic field at the CMB from 1200BC to 2000AD

Movie of the time-evolution (from 1880 to 2015) of flow in the Earth's core, built from Gillet_gnm_2019 model (Gillet et al, 2019), using the webgeodyn platform. Orthographic map projection (northern hemisphere).

Time evolution of flow in the Earth's core

The DTS experiment

Henri-Claude NATAF — 2020-10-12T06:23:47Z

The DTS experiment is listed in the PATSTEC catalog of contemporary scientific and technical heritage.

Le coeur de DTS au coeur de l'exposition Sauve-garde ! de l'UGA au printemps 2025 (photo Yue-Kin Tsang)

see a brief presentation of DTS in the historical sketch of the geodynamo team.

ESA project '4D-Earth Core + SWARM'

Henri-Claude NATAF, Nicolas GILLET — 2020-07-13T09:25:25Z

- Completed projects

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?

test

Henri-Claude NATAF — 2020-04-09T13:23:55Z

- On-going projects

current post-doc proposals

2020-03-12T15:21:35Z

- Internships, PhD, post-doc offers