In "Nature Communications": Computer simulations make turbulent mixing more predictable

When a drop of paint is released into a flow of water, its outer shape visibly dissolves until finally a diffuse cloud of paint is left drifting on the surface of the water. How the drop's fine inner structures change in the course of this process remains hidden to the eye. The authors of the study succeeded in making the evolution of these fine structures visible in computer simulations. For their study, they chose the simplest possible structures as examples: small rings, also known as "material lines" in fluid physics. "As the computer simulations show, these rings are strongly deformed in a turbulent flow. In a very short time, a highly complex structure resembling a ball of wool forms out of each individual ring. The degree to which this ball is knotted reflects the extent to which turbulent mixing has proceeded. It accurately reflects the evolution of the mixing," says Prof. Dr. Michael Wilczek, Chair of Theoretical Physics at the University of Bayreuth.

Based on the knowledge gained in these simulations, the scientists were able to systematically describe the geometric properties of the complex tangles. "When we took a closer look at the geometry of the deforming material lines, we immediately noticed that their curvature followed a clearly defined statistical distribution - even though the lines looked more and more complicated over time," reports Bayreuth physics PhD student Lukas Bentkamp, first author of the study. The research team uncovered the mechanisms of turbulent deformation and thus developed a mathematical theory from which statistical laws can be derived. "So in a statistical sense, we were able to discover and explain regular processes in the turbulent mess," Bentkamp says. The research results achieved in Bayreuth and Göttingen represent a major contribution in the quest for a universally applicable theory of turbulent mixing, and help to better understand mixing processes in the environment.

Video “From a simple ring to a complex tangle”:
https://www.youtube.com/watch?v=1FK2nfswz1c

Publication:
Lukas Bentkamp, Theodore D. Drivas, Cristian C. Lalescu and Michael Wilczek: The statistical geometry of material loops in turbulence. Nature Communications 13, 2088 (2022). https://doi.org/10.1038/s41467-022-29422-1