- more normal than expected?

August 20, 2019

The flight through our atmosphere can be quite turbulent for an insect: In addition to long periods of calm flight, extreme accelerations can occur from time to time, especially when the insect encounters small-scale turbulence in the form of vortices. Such vortices also play a major role in the formation of rain, for example, as they significantly influence the collision of very small droplets in clouds, from which falling raindrops eventually develop. Describing and predicting the frequency of these events is therefore an important goal of turbulence research. In a study now published in Nature Communications, Dr. Michael Wilczek and his team at the Max Planck Institute for Dynamics and Self-Organization have succeeded in disentangling the complex statistics of fluid particles.

The velocity changes of particles in turbulent flows depend strongly on the time scale considered. Statistically, extreme changes occur particularly frequently on small scales. This phenomenon can be characterized as a deviation from a Gaussian normal distribution, also known as a bell curve. Because such normal distributions are considered to be particularly simple, the researchers now looked into the question of whether turbulence is perhaps more "normal" than previously thought. "If we categorize the turbulence after the acceleration events, as they occur in vortices, we suddenly get a very simple picture. The distribution of turbulent fluctuations along particle paths then follows a Gaussian normal distribution," says Lukas Bentkamp, master's student at the University of Göttingen and lead author of the study.

Fluid particles in turbulent flows exhibit very entangled trajectories when encountering small-scale vortices (displayed in blue).

To discover this, millions of particle paths had to be analyzed and systematically sorted into different categories. Co-author Dr. Cristian Lalescu adds: "Only high-resolution computer simulations have made this insight into the fascinating fine-scale structure of turbulence possible." As the study demonstrates, this observation opens up a variety of new modeling approaches for the statistical description of turbulence. In the future, these could help, for example, to make better predictions for the occurrence of extreme fluctuations in the atmosphere or to better understand how rain forms.

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