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

June 08, 2011

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.

The simulation of turbulent flows is now becoming easier

Bodenschatz and his team observed an analogous effect in turbulent water. The flow stretched the tetrahedron so that it became thinner. In addition, the tetrahedron’s axis of rotation aligned so that it was parallel to the original stretching direction of the flow. The stretched tetrahedron’s speed of rotation ultimately increased. “All the while, the angular momentum was conserved,” says Bodenschatz. In this way, the observed dynamics correspond with a pirouette of a spinning ice-skater. Bodenschatz and his colleagues thus refer to this as the “pirouette effect”.

The fact that the angular momentum of the vortex is conserved in the centre of a turbulent liquid was something that surprised the physicists. “We do not yet understand why this is the case,” says Bodenschatz. The vortices in the chaos of a turbulent flow should actually experience torsional forces that change their angular momentum.  The pirouette effect shows that “a relatively high degree of order” prevails within the chaos of a turbulent flow, says the physicist.

This order in chaos can be seen on different size scales. Using the method outlined above, the Göttingen-based physicists studied vortices with diameters ranging from a few millimetres to several centimetres. “All demonstrated the pirouette effect,” says Bodenschatz. “Our result confirms the energy cascade model,” says the physicist. Since the 1930s, researchers have acted under the assumption that the energy cascade was heavily influenced by vortex dynamics. According to this concept, the vortices in the flow stretch and rotate faster around their longitudinal axis – thus becoming instable and breaking down into smaller vortices, which then undergo the same process until a cascade is reached with very small vortices.

In the last thirty years or so, however, this notion appeared to be refuted by calculations according to which the axis of rotation never aligns with the strongest stretching direction of the flow, but rather remains vertical to this. “These calculations, however, only examined snap shots of the flow field”, says Bodenschatz. They represent, so to speak, snapshots. “For the first time, on the other hand, we monitored how vortices float with the liquid,” says the physicist. This is the only way to trace the development of a vortex over time. An analysis of a single floating particle in the flow has now confirmed the pirouette effect, something that has only been an assumption up until now.

Bodenschatz sees this result as a step towards solving an important problem in the computer-based simulation of turbulent flows. “Many aspects of turbulent flows can already be simulated, but we have not yet been able to simulate how different size scales interact with one another.” He believes that this could change if we have a better understanding of the dynamics of vortices of different sizes.

CM

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