Our work on the intermittency of circulation has been published in Physical Review X

Quantum and classical turbulence are more similar than what we could have though

A superfluid vortex tangle composed of thousands of quantum vortex filaments (in yellow). The small box in the top left panel is enhanced in the top right figure and reproduced in the bottom panel. Dot corresponds to vortices coloured accordingly their orientation respect to the plane

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.


  1. For example, a hundred micrometres in a turbulent superfluid helium flow. ↩︎

Giorgio Krstulovic
Giorgio Krstulovic
Chargé de recherche CNRS

My research interests include classical and quantum turbulence, vortex dynamics and wave turbulence.