When we think of a tornado, we often imagine a long filament moving through space, dragging everything in its path. These tornadoes or eddies, called vortices by physicists, are ubiquitous in turbulent flows, such as one observed in the atmosphere, the oceans, or in a simple cup of coffee stirred by a spoon. Indeed, if we look at a turbulent fluid at small scales, we will see forests of eddies oriented in all possible directions.

If one wants to understand turbulence, it is natural to try to “count” how many vortices one could observe in a region of a certain size, and try to quantify the collective speed of rotation of this region. To do so, we can define a quantity, called circulation, which depends on the scale of interest and all the vortices within that region. In a turbulent fluid, the circulation fluctuates enormously and can take extreme values.

In the quantum world, we also find vortices among a very exotic class of fluids: the superfluids. A superfluid flows without any friction, because thanks to quantum effects, their viscosity is identically zero. They are also found in the laboratory, in experiments with helium or with certain atomic gases at very low temperatures. A superfluid can also easily become turbulent. As in classic turbulence, we can try to count the vortices and calculate their circulation. In the case of superfluids, this is particularly interesting because the circulation takes discrete values ​​as a consequence of quantum effects. The figure above shows a visualisation of turbulent superfluid obtained from a numerical simulation of our team. Each small yellow filament corresponds to a quantum vortex that interacts with all the others. The orientation or sense of rotation of each vortex, is represented by the two coloured dots in the bottom panel.

In this work, we have shown quantitatively that classical and quantum turbulence have the same statistical properties of circulation at scales in the classical range ¹, including the most violent fluctuations of the flow. On the other hand, they show significant differences at smaller scales as in the classical case, smalls scale dynamics is governed by viscous effects whereas, in superfluids, quantum effects are dominant. The results of this work, published in Physical Review X, reinforce the idea that quantum turbulence is sort of the skeleton of classical turbulence.

UPDATE

As a follow up of this work, we have published a new work on Nature Communications. In this article we explore further the the similarities and differences between quantum and classical turbulence. This new work, a bit more theoretical, provides some insight to understand intermittency in quantum fluids.

External links

• The results of this work have been also highlighted in the news of Observatoire de la Côte d’Azur, the Universté Côte d’Azur and the Institut national des sciences de l’Univers (INSU).
• The results of the Nature Communications paper were also highlighted in the news of the Institut national des sciences de l’Univers (INSU).