Home Science & Technology A new dynamical structure of turbulence discovered by physicists

A new dynamical structure of turbulence discovered by physicists

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The researchers’ experiment featured transparent walls to provide full visual access and used state-of-the-art flow visualization. Author: Michael Schatz

The findings reveal a new “road map” for turbulence research with a wide range of applications, including more accurate weather forecasts and improved fuel efficiency for cars and planes.

Although most people don’t think about it, turbulence plays a key role in our daily lives. It creates bumpy airplane rides, affects the weather and climate, limits the fuel efficiency of the cars we drive, and affects clean energy technologies. However, scientists and engineers puzzle over ways to predict and modify turbulent fluid flows. In fact, it has long remained one of the most challenging problems in science and technology.

A new dynamic framework for an experimental turbulence setup

The setup allowed the researchers to reconstruct the flow by tracking the movement of millions of suspended fluorescent particles. Author: Michael Schatz

Now physicists at Georgia Tech have demonstrated—numerically and experimentally—that turbulence can be understood and quantified using a relatively small set of special solutions to the governing equations of fluid dynamics that can be pre-computed for a specific geometry, once and for all.

“For almost a century, turbulence has been described statistically as a random process,” said Roman Grigoriev. “Our results provide the first experimental illustration that, on suitably short time scales, the dynamics of turbulence is deterministic—and connects it to the underlying deterministic equations.”

The results were published on August 19, 2022 Proceedings of the National Academy of Sciences. The research team was led by Grigoriev and Michael Schatz, professors in the School of Physics at Georgia Tech, who have collaborated on various research projects over the past two decades.

Schatz and Grigoriev were joined by School of Physics graduate students Chris Crowley, Joshua Pugh-Sanford, and Wesley Toler. Also on the team was Michael Krieger, a Sandia National Laboratory postdoctoral fellow who developed the numerical solvers in the study as a graduate student at the Georgia Institute of Technology.

A new “road map” for turbulence research

Quantitatively predicting the evolution of turbulent flows—and, in fact, almost any of their properties—is very difficult. “Numerical modeling is the only reliable forecasting approach available,” said Grigoriev. “But it can be very expensive. The goal of our research was to make forecasting less expensive.”

A team of researchers created a new “road map” of turbulence by looking at a weakly turbulent flow that was confined between two independently rotating cylinders. This gave the team a unique way to compare experimental observations with numerically calculated flows due to the absence of “end effects” present in more familiar geometries such as pipe flow.

A new dynamical framework for the turbulence scheme

Physicists research scheme. Author: Michael Shatz, Roman Grigoriev

“Turbulence can be seen as a car moving on roads,” said Grigoriev. “Perhaps an even better analogy is a train that not only follows a railroad on a prescribed schedule, but also has the same shape as the railroad it travels on.”

The experiment had transparent walls to allow full visual access. It also used state-of-the-art flow imaging to allow physicists to reconstruct the flow by tracking the movement of millions of suspended fluorescent particles. In parallel, advanced numerical methods were used to calculate recurrent solutions of the differential equation with partial derivatives (the Navier-Stokes equation) governing fluid flows under conditions that closely match the experiment.

It is well known that turbulent fluid flows exhibit a set of patterns, referred to in the field as “coherent structures”, which have a well-defined spatial profile but appear and disappear in an apparently random manner. Analyzing their experimental and numerical data, the scientists found that these flow patterns and their evolution resemble those described by the special solutions they calculated. These special solutions are both periodic and unstable. This means that they describe repeating patterns of flow over short periods of time. Turbulence tracks one such decision at a time, explaining which patterns might emerge and in what order.

Recurrent solutions, two frequencies

“All the recurrent solutions we found in this geometry turned out to be quasi-periodic – that is, characterized by two different frequencies,” said Grigoriev. One frequency described the total rotation of the flow about the axis of symmetry of the flow. Another frequency described changes in the shape of the flow pattern in a frame of reference that rotates simultaneously with the pattern. Corresponding threads are periodically repeated in these frames, which rotate simultaneously.

“We then compared the turbulent flows in experiment and direct numerical simulations with these periodic solutions and found that the turbulence carefully follows (tracks) one periodic solution after another as long as the turbulent flow persists,” Grigoryev said. “Such qualitative behavior was predicted for low-dimensional chaotic systems such as the famous Lorentz model, derived six decades ago as a greatly simplified model of the atmosphere.”

Roman Grigoriev and Michael Schatz

Roman Grigoriev (left) and Michael Shatz. Author: Georgia Tech

The study represents the first experimental observation of recurrent chaotic motion tracking solutions actually observed in turbulent flows. “Dynamics of turbulent flows are, of course, much more complicated due to the quasi-periodicity of recurrent solutions,” Grigoriev added.

“Using this method, we have convincingly shown that the organization of turbulence in both space and time is well captured by these structures,” the researchers said. “These results lay the foundation for representing turbulence in terms of coherent structures and exploiting their persistence over time to overcome the disruptive effects of chaos on our ability to predict, control, and create fluid flows.”

A new dynamical framework for 3D fluid flows

These findings directly affect the community of mathematicians, physicists and engineers still trying to understand fluid turbulence, which remains “perhaps the biggest unsolved problem in all of science,” Grigoryev said.

“This work builds on and extends previous work by the same group on fluid turbulence, some of which has been reported at Georgia Tech in 2017“, he added. “Unlike the work discussed in this publication, which focuses on idealized two-dimensional fluid flows, the current study addresses practically important and more complex three-dimensional flows.”

Ultimately, the team’s research lays a mathematical foundation for fluid turbulence that is dynamic rather than statistical in nature. Thus, it has the ability to make quantitative predictions that are critical for a variety of applications.

“This can give us an opportunity to improve a lot[{” attribute=””>accuracy of weather forecasts and, most notably, enable prediction of extreme events such as hurricanes and tornadoes,” said Grigoriev. “Dynamical framework is also essential for our ability to engineer flows with desired properties, for instance, reduced drag around vehicles to improve fuel efficiency, or enhanced mass transport to help remove more carbon dioxide from the atmosphere in the emerging direct air capture industry.”

Reference: “Turbulence tracks recurrent solutions” by Christopher J. Crowley, Joshua L. Pughe-Sanford, Wesley Toler, Michael C. Krygier, Roman O. Grigoriev and Michael F. Schatz, 19 August 2022, Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2120665119

Funding and acknowledgments: The researchers thank Marc Avila for sharing his Taylor–Couette flow code, and gratefully acknowledge financial support by Army Research Office under Grants W911NF-15-1-0471 and W911NF-16-10281 and by NSF under Grant CMMI-1725587.

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