The pirouette effect in the chaos of turbulence

Findings on how vortices behave in a turbulent flow could facilitate the simulation of clouds in climate models

The quick mixing of coffee and milk after stirring or the formation of raindrops in clouds: these are just two of many phenomena in which turbulent flows play a decisive role. Researchers at the Max Planck Institute for Dynamics and Self-Organization and the Ecole Normale Superieure de Lyon have now discovered that the seemingly random turbulent flows actually have an astonishingly uniform structure. According to the findings, vortices are a basic ingredient of turbulent flows and they behave similarly to an ice-skater performing a pirouette – a technique whereby the skater bends his or her arms to increase the speed of rotation. The researchers monitored this pirouette effect in vortices of various sizes in a turbulent liquid. In doing so, they unravelled a mystery that has confounded turbulence researchers for decades – namely the question of how energy flows from large to ever-smaller vortices, and how it is ultimately converted to heat in the smallest vortices.

As far back as the first half of the last century, physicists were already exploring the question of how turbulent flows convert the energy of a directional flow into omni-directional heat energy. The explanation they came up with was the so-called “energy cascade” concept – a concept according to which the kinetic energy, e.g. of a river, initially flows in large, rapidly rotating vortices when cascading down a waterfall. The large vortices then break down into smaller vortices, which in turn break down into even smaller ones. The smaller the vortices become, the slower the speed of their rotation. In the slowly rotating mini-vortices, the strength of the friction is such that the kinetic energy is ultimately converted into heat energy.

This energy cascade process is used by people on a daily basis, for example in mixing processes: when stirring milk in coffee, the milk flow initially triggered by the spoon is converted within seconds to a directionless, even distribution of tiny milk drops. The base materials of chemical reactions are also mixed with the aid of turbulent flows, the process thereby being much faster than if the materials are not mixed.

Turbulent flows from the perspective of floating particles

However, researchers do not yet understand the mechanisms of turbulent flows. Such an understanding could greatly simplify computer modelling of turbulent processes and thus, for example, the simulation of clouds in climate models. Physicists Eberhard Bodenschatz and Haitao Xu from the Max Planck Institute for Dynamics and Self-Organization in Göttingen and Alain Pumir from the Ecole Normale Superieure de Lyon have now taken an important step towards understanding turbulent flows. By studying a single floating particle in a turbulent flow for the first time, they discovered a basic ingredient in turbulent flows.

To this end, they used a high-speed camera to monitor polystyrene particles in a turbulent water flow, which were illuminated by a very bright laser. When analysing the images, they singled out a particle surrounded by three further particles. These particles were separated by an equal distance so that they formed a tetrahedron. They observed how the positions of the particles with respect to one another changed over time, namely how the tetrahedron in the turbulent liquid changes shape and how it rotates. This process involved extreme time-lapse recordings of 30,000 images per second.

The result astonished the physicists: the particles effectively performed a dance similar to the pirouette in ice-skating. When an ice-skater bends his or her arms while spinning, the speed of the rotation drastically increases. The reason for this is the conservation of a physical variable known as the angular momentum. A particle of mass located outside the axis of rotation exerts greater resistance to the rotation than a particle of mass located within the axis, which means that the speed of the rotation increases as the particle of mass moves inwards.