Fiber tracking method offers important new insights into turbulence

From heart murmurs and pipeline oil transportation, to bumpy planes and pollutant dispersal, turbulence plays an important role in many everyday events. But despite being commonplace, scientists still don’t fully understand the seemingly unpredictable behavior of eddies and eddies in turbulent flows.

Now, a new technique for measuring turbulent flows has been developed by an international collaboration of scientists from the Okinawa Institute of Science and Technology Graduate University (OIST) in Japan, along with the University of Genoa, Italy, KTH Stockholm, Sweden and ETH Zurich, Switzerland. By using fibers rather than particles – the usual method of measurement – the researchers were able to get a more detailed picture of turbulent flows. Their method was reported on September 17 in the newspaper, Physical examination X.

“Turbulence is a very unique and complicated phenomenon, it has even been called the last unsolved problem in classical physics,” said Dr. Stefano Olivieri, postdoctoral researcher in the Complex Fluids and Flows Unit at OIST, who was one of the authors of the study. “It’s hard to predict, hard to simulate and hard to measure.”

The measurement of turbulent flows is a pressing challenge for physicists for many reasons. Not only is turbulence characterized by its chaotic and random nature, but it also occurs on multiple scales at once. In turbulent flows, the swirling vortices of fluid break up into smaller and smaller vortices, until eventually the vortices are so small and viscous that the fluid’s kinetic energy is transferred to the surroundings as heat .

Currently, the most common way to measure turbulent flows is to track the movement of particles, called tracers, that are added to the fluid. These particles are tiny and of similar density to the fluid, and therefore move at the same speed and in the same direction as the flow.

But to observe how each vortex of fluid moves, it is not enough to watch how a particle moves. Physicists need to be able to determine how two particles far apart move relative to each other. The smaller the vortex, the closer the two particles must be to characterize the movement of the vortex.

To make matters more difficult, one of the defining characteristics of turbulence is its diffusivity – turbulent flow will spread over time, as will tracers, especially in open flows, such as an ocean current. In many cases, tracers can quickly spread too far to measure eddy behavior.

“Each tracer particle moves independently of each other, so it takes a lot of tracer particles to find the ones that are the right distance apart,” explained Professor Marco Rosti, who leads the OIST Complex Fluids and Flows.

“And too many tracer particles can actually disrupt the flow,” he added.

To circumvent this problem, the research team developed an innovative and simple solution to the problem: to use fibers instead of tracer particles.

The researchers created a computer simulation where fibers of different lengths were added to a turbulent flow. These fibers were rigid, which kept the ends of each fiber at a fixed distance. By tracking how each fiber moved and rotated in the fluid over time, the researchers were able to create a picture that encompassed the full scale and structure of turbulent flow.

“Using stiff fibers, one can measure the difference in speed and direction of flow at two points that are distant from each other, and one can see how these differences change as a function of the scale of the vortex. The shortest fibers also allowed us to accurately measure the rate at which the kinetic energy of the fluid is transferred from the larger to the smaller scale, where it is then dissipated by heat. This value, called the dissipation rate of energy, is a crucial quantity in the characterization of turbulent flows,” said Professor Rosti.

The researchers also performed the same experiment in the lab. They made two different fibers, one made from nylon and the other from a polymer called polydimethylsiloxane. The team tested these two fibers by adding them to a water tank containing turbulent water and found that the fibers gave similar results to the simulation.

However, using stiff fibers comes with an important caveat, the scientists pointed out, because the overall movement of the fiber ends is limited.

“Due to the stiffness of the fibers, the ends of the fibers cannot move towards each other, even if that is the direction of flow. This means that a fiber cannot fully represent the motion of the flow in the same way that tracer particles can,” explained Dr. Olivieri. “So before we even started simulations or experiments in the lab, we first had to develop a proper theory that took into account these movement limitations. This was perhaps the most difficult part of the project.”

The researchers also measured the same turbulent flow in the lab in a conventional way, adding a high concentration of tracer particles to the water reservoir. The results obtained from the two different methods were similar, verifying that the fiber method and the newly developed theory gave accurate information.

In the future, the researchers hope to expand their method to incorporate flexible fibers that have less restriction on their movement. They also plan to develop a theory that can help measure turbulence in more complex non-Newtonian fluids that behave differently from water or air.

“This new technique has a lot of exciting potential, especially for scientists studying turbulence in large open flows like ocean currents,” Prof Rosti said. “And being able to easily measure quantities that were previously difficult to obtain brings us one step closer to fully understanding turbulence.”