CNRSNon-linear physics and Turbulence studies
non-linear physics and turbulence, CNRS, Grenoble [P.-E. Roche]

Various written ressources


Conference proceedings

References to some old conference proceedings may be found here


Few popularization science writting

Listening to quantum turbulence with second sound tweezers

written by E. Woillez [an highlight for EPL 134:46002 (2021)]

Second sound tweezers

A 250 microns size second sound tweezers

Quantum turbulence displays the spectacular property to dissipate energy without viscosity. This process is intimately related to the dynamical structure of the flow at very small scale. Existing velocity sensors are too large to resolve the crossover scale between classical and quantum physics. The propagation of temperature waves called “second sound” is an alternative way to directly probe the quantum scales of the flow. Using micro-fabricated second sound tweezers, researchers from Institut Neel report the first characterization of quantum scale fluctuations in intense turbulent flows, close and far below the superfluid transition.

La mémoire des écoulements superfluides

based on [J. Bertolaccini et al, PRF 2:123902 (2017) ]

Memory and Entrance effect in Superfluid counterflows

Effect d'entrée d'un écoulement superfluide

Un sillage turbulent est d’autant plus étendu que la viscosité du fluide est faible. Des simulations d’un écouleent sans viscosité d’hélium superfluide révèlent un subtil effet de sillage permettant d’expliquer de nombreuses expériences contradictoires.

Après sa rencontre avec les piles d’un pont, une rivière présente une turbulence sur la suite de son parcours. Ce sillage est la mémoire des perturbations subies en amont, près des piles. Cette mémoire s’estompe sur une distance d’autant plus grande que la viscosité du fluide est faible. Qu’en est-il d’un écoulement à viscosité nulle, pour un superfluide ?
L’étude des écoulements superfluides est devenue accessible aux physiciens à partir des années 1930 en utilisant de l’hélium liquide à des températures proches du zéro absolu (-273 °C). Cependant, les nombreuses expériences menées ont conduit à une grande disparité des mesures, souvent inconciliables. En s’appuyant sur des simulations numériques, on vient de découvrir un effet mémoire insoupçonné dans les écoulements superfluides. Ainsi, seules les mesures effectuées dans des conduites suffisamment longues peuvent être réconciliées, alors que les autres mesures sont inévitablement entachées d’effets mémoire relatifs aux conditions de démarrage de l’écoulement. Cette découverte a été parfaitement corroborée par l’analyse détaillée des conditions expérimentales des études précédentes, et permet désormais de mieux définir le dimensionnement des futures expériences sur les superfluides, et d’espérer (enfin) comprendre les mystérieuses instabilités de ces écoulements. En ingénierie, les écoulements superfluides jouent un rôle essentiel dans le refroidissement des bobines supraconductrices.

Area of Turbulence

by Anaïs Schaeffer [CERN Bulletin Issue No. 32-33/2015]
Monday 3 August 2015

CERN Euhit cryogenic helium jet

Fig.: The last day of data collection, July 2015.

As a member of the EuHIT (European High-Performance Infrastructures in Turbulence) consortium, CERN is participating in fundamental research on turbulence phenomena. To this end, the Laboratory provides European researchers with a cryogenic research infrastructure, where the first tests have just been performed....
CERN has a unique cryogenic facility in hall SM18, consisting of 21 liquid-helium-cooled test stations. While this equipment was, of course, designed for testing parts of CERN's accelerators, it can also be used for other laboratory experiments, notably for studying “very intense turbulence” in fluids.
Very intense turbulence is a natural phenomenon observed in numerous situations – in the atmosphere and in the ocean, in the slipstream of planes and trains, and even in stars – but it is very difficult to study. (to continue)


The turbulent superfluid cascade [ Institut Néel Highlights 2012 ]

liquid helium wind-tunnel TOUPIE

Fig. The TOUPIE wind-tunnel. At right: details of the high-stiffness, low-conductivity mechanical structure (top); cryogenic propeller specially optimised for liquid helium (middle); and probe holders with miniature Pitot-tube velocity sensors (bottom).

Stirring a honey pot with a spoon is awkward because the fluid viscosity damps the flow very efficiently. By contrast, in a less viscous fluid such as coffee in a cup, a slight movement of a spoon will generate eddies of different sizes. If the fluid is even less viscous, or if the mechanical stirring is more intense, a hierarchy between eddies of different sizes appears: the flow is turbulent. In 1941, the Russian mathematician Andrei Kolmogorov described this hierarchy of eddies with the image of an energy cascade : mechanical stirring feeds the largest eddies, which transfer their energy to smaller eddies and so on until the viscosity effectively inhibits any further whirling motion and dissipates energy into heat.
What does this cascade of energy become in a fluid with zero viscosity ? An exotic liquid allows us to address this question experimentally : superfluid helium. Below 2.17 K, liquid helium enters a quantum phase, the "He-II" state. It then acquires the remarkable capability of flowing without experiencing any viscosity. Exploring the turbulent cascade of a superfluid, however, raises two experimental challenges: creating a suitable cryogenic flow and probing the velocity fluctuations in the superfluid.
To answer these questions, the Institut Néel has developed a cryogenic "wind tunnel". We have named this apparatus "TOUPIE" (our acronym for “TOUrne Par l’Intérieur et l’Extérieur”, refering to the rotational degrees of freedom in the design of the experiment, and also the French word for a spinning top). It produces a closed, permanent flow of liquid helium along a record path of 2 metres (see Fig. 1) at temperatures from 4 K down to 1.5 K. It can operate with superfluid helium (He-II), and also with "viscous" liquid helium (the "He-I" state, above 2.17 K), thereby allowing direct comparison between the two cascades. The second challenge was to improve significantly the spatial resolution of the best probes for measuring velocity in a superfluid. Among the innovative sensors devised and developed, the one shown in Fig. 2 is a micro-machined silicon cantilever, coupled to an ultra-sensitive superconducting resonator diverted from its original astrophysics destination: the detection of cosmic particles.
The combination of this unique cryogenic wind tunnel with the smallest superfluid probes allowed us to compare the turbulent cascades of a classical fluid with those of a superfluid, with an unprecedented resolution. In particular, we found the first direct evidence that superfluid eddies can cascade from large to small scales in a fashion similar to that of classical eddies. This evidence came from the Kármán-Howarth "4/5 law", the only exact relation in turbulence (named after a factor 4/5 in the equation that relates the amount of energy carried by the turbulent cascade and a dissymmetric statistics of the velocity gradients). Comparing our data with the Kármán-Howarth law, we found that this law remains valid in a superfluid.
The next challenge is to understand how, in the superfluid, a non-viscous dissipation process replaces the effects of viscosity, especially in the limit of relatively low temperatures (~ 1 K). A second version of the TOUPIE wind-tunnel is in preparation to reach this lower temperature range.


Local velocity probe for cryogenic helium [ Renatech newsletter, June 2011 ]

micro-cantilever anemometer

Fig. Micro-machined velocity probe based on the deflection of a 1 micron thick, 100 micron wide, silicon cantilever by the moving fluid. Main image shows the V-shaped probe-holder with the cantilever at its tip. The upper insert shows a general top-view onto the probe holder. The bottom insert is a zoomed top-view of the cantilever itself, carrying a circuit which is part of a superconducting resonator whose frequency varies with the cantilever's deflection. Device fabricated at Grenoble's Plateforme Technologique Amont.

The experimental study of superfluid turbulence, ie. the hydrodynamics of strongly stirred liquid helium at very low temperature (T < 2.17 K) requires specifically designed local probes. These probes need to be both very small and highly sensitive to measure the small scale velocity fluctuations that are fast and have a low amplitude.

To do this, we designed a cryogenic velocity probe based on a cantilever. The sensitive element of the probe is the cantilever tip (300 µm long, 100 µm wide, 1 to 10 µm thick), etched in a bulk silicon wafer using fluoride Deep Reactive Ion Etching. This tip is immersed in the bulk of a flow and gets deflected by the incoming fluid. The amplitude of this deflection is proportional to the square of the flow velocity in the vicinity of the cantilever tip. A precise measurement of the deflection fluctuations is achieved using a radio-frequency superconducting niobium LC resonator sputtered on the tip whose resonance frequency shifts when the cantilever is elongated.

This technique prevented us to allow the presence of any disordered dielectric material on the sample because they would lead to phase noise of the LC resonator. This precluded us from using an oxide barrier layer. Therefore we had to devise a way to properly tune the thickness. We used the etching machine refrigerating helium leak rate as an progress indicator. The first prototype has been cooled down and tested recently and showed good performances, similar to these of the best probes known to work in superfluid helium, and we believe that we can improve them even further in a near future.




PhD thesis

Modélisation et simulation des écoulements de contre-courant de l’hélium superfluide par la méthode Boltzmann sur réseau
Jonathan BERTOLACCINI, PhD thesis of ENS de Lyon In co-direction with E. Lévêque, who was the lead advisor
archive TEL

Quantum turbulence versus Classical turbulence
Julien SALORT, PhD thesis of Grenoble university
archive TEL

Convection turbulente dans une cellule de Rayleigh-Bénard cryogénique : de nouveaux éléments en faveur du Régime Ultime de Kraichnan, PhD thesis of the Université Joseph Fourier
archive TEL

High cryogenic Reynolds experiment : GReC
Sylvain PIETROPINTO, PhD thesis of the Université Joseph Fourier

Turbulent convection in cryogenic Rayleigh-Bénard cells
Philippe-E. ROCHE, PhD thesis of the Université Joseph Fourier
archive TEL

Towards dissipative scales in a gaseous Helium jet at low temperature
Olivier CHANAL, PhD thesis of the Université Joseph Fourier

Etude du régime turbulent en convection de Rayleigh-Bénard dans l'hélium liquide ou gazeux autour de 5 K
Xavier CHAVANNE, PhD thesis of the Université Joseph Fourier

Turbulence dans un jet d'hélium à basse température>
Antoine NAERT, PhD thesis of the Université Joseph Fourier

Etude de la turbulence dans un jet d'hélium gazeux à basse température
Benoit CHABAUD, PhD thesis of the Université Joseph Fourier

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