Turbulence plays a key role in everyday human life: it affects flights, weather and climate, and
Now physicists from the Institute of TechnologyGeorgia have demonstrated - numerically and experimentally - that turbulence can be understood and quantified with a relatively small set of ad hoc solutions to the fundamental equations of hydrodynamics. They can be precomputed for a particular geometry.
The results of the study are published in the journalProceedings of the National Academy of Sciences. The research team was led by Roman Grigoriev and Michael Schatz, professors in the School of Physics at the Georgia Institute of Technology.
Scheme of the study of physicists. Photo: Michael Schatz, Roman Grigoriev
Quantitatively predict the evolution of turbulentcurrents, and almost any of their properties, is quite complex. Numerical modeling is the only reliable forecasting approach available. The problem is that it “can be terribly expensive,” the study authors explain. The goal of the new work is to make forecasting less expensive.
New experiment of scientists
Researchers have created a new "road map"turbulence by studying a weak turbulent flow between two independently rotating cylinders. So physicists have created a unique way to compare experimental observations with numerically calculated fluxes. All thanks to the lack of end effects.
“Turbulence can be thought of as a trainwhich not only follows the railroad according to the prescribed schedule, but also has the same shape as the railroad on which it travels, ”the scientists explain.
In the experiment, physicists used transparentwalls that provide full visual access. So they were able to track the movement of millions of suspended fluorescent particles. In parallel, the scientists used advanced methods to compute recurrent solutions to a partial differential equation (the Navier-Stokes equation) that governs fluid flows under conditions exactly consistent with experiment.
The researchers' experiment used transparent walls for full visual access and state-of-the-art flow visualization. Photo: Michael Schatz
It is well known that turbulent fluid flowsdemonstrate a set of patterns that are called coherent structures. Not only do they have a well-defined spatial profile, they also appear and disappear in a seemingly random way. Analyzing experimental and numerical data, physicists have found that flow patterns and their evolution resemble those described by ad hoc solutions (which they have calculated). It is important that they are recurrent and unstable. And, therefore, they describe repeating flow patterns at short intervals. Turbulence tracks one such decision after another, which explains what patterns might appear and in what order.
What have the scientists done?
All recursive solutions that scientists have foundturned out to be quasi-periodic, i.e., characterized by two different frequencies. One frequency described the general rotation of the flow pattern around the symmetry axis of the flow, and the other described changes in the shape of the flow pattern in the frame of reference. The corresponding flows are periodically repeated in co-rotating patterns.
The physicists then compared the turbulent flows inexperiment and direct numerical simulation with repeated solutions. It turned out that turbulence accurately tracks one repetitive decision after another, as long as the flow is maintained. Such behavior has already been predicted for low-dimensional chaotic systems, such as the famous Lorentz model.
The setup allowed the researchers to reconstruct the flow by tracking the movement of millions of suspended fluorescent particles. Photo: Michael Schatz
Thus, scientists experimentally observedrecurrent solutions for tracking chaotic motion in turbulent flows. However, they noted that the dynamics of turbulent flows is much more complicated due to the quasi-periodic nature of the recurrent solutions.
However, they showed that the organizationturbulence both in space and in time is well captured by these structures. These results are useful to represent turbulence in terms of coherent structures and use their constancy over time. The goal is to overcome the destructive effect of chaos on the ability of physicists to predict, control and design fluid flows.
Where it leads?
The results of the experiment will affect the communityphysicists, mathematicians and engineers who are still trying to understand fluid turbulence. It is considered perhaps the biggest unsolved problem in all of science, the authors of the study emphasize.
Ultimately, the experiment of scientists laysthe mathematical basis for fluid turbulence, which is dynamic in nature, not statistical. This will enable quantitative predictions that are critical for various applications.
This will not only improve the accuracy of dailyweather forecasts, but most importantly, extreme events such as hurricanes and tornadoes. The dynamic structure is also important for scientists who are trying to design flows with the desired properties. For example, physicists will be able to reduce drag around vehicles to improve fuel efficiency.
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