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