Turbulence plays a key role in human daily life: it affects flight, weather and climate, as well as clean energy technologies; it also limits the fuel efficiency of cars; however, scientists and engineers have been breaking their minds for a long time on how to predict and change turbulencel fluid flows; it has remained one of the most difficult problems in science and technology for a long time.
The physicists from Georgia's Institute of Technology have now demonstrated — numerically and experimentally — that turbulence can be understood and quantified with a relatively small set of special solutions to basic hydrodynamic equations. They can be pre-calculated for specific geometry.
The results of the study were published in the journal Proceedings of the National Academy of Sciences, led by Roman Grigoriev and Michael Shatz, Professor of the School of Physics of the Georgia Institute of Technology.
Quantification of the evolution of turbulence, and almost all of its properties, is difficult, and numerical modelling is the only reliable approach available for forecasting. The problem is that this "may be extremely expensive" is explained by the authors of the study. The purpose of the new work is to make the projection less costly.
A New Experiment of Scientists
Researchers have created a new "road map" of turbulence, studying the weak turbulence flow between two independently rotating cylinders, so physics has created a unique way to compare experimental observations with numerically calculated flows, all due to the absence of end effects.
"Turbulency can be seen as a train that not only follows the railway as scheduled, but also has the same shape as the railway on which it is travelling," the scientists explain.
In the experiment, physicists used transparent walls that provide full visual access, so they were able to trace the movement of millions of suspended fluorescent particles, and in parallel, scientists used advanced techniques to compute recurring solutions to equations in private derivatives that control liquid flows under conditions that are exactly consistent with the experiment.
It is well known that turbulent fluid flows show a set of pathogens that are called coherent structures. They not only have a clearly defined spatial profile, they also appear and disappear in a seemingly random way. By analysing experimental and numerical data, physicists have found that current models and their evolution resemble those described by special solutions. It is important that they are recursive and unstable. This means that they describe recurring current patterns at short intervals. Turbulentity tracks one such decision after another, which explains what patterns can appear and in what order.
What did scientists do?
All of the recurring solutions that scientists found were quasi-periodic, i.e. two different frequencies. One frequency described the total rotation of the current pathometer around the flow symmetry axis and the other the changes in the shape of the current pathometer in the reference system. The corresponding flows are periodically repeated in the co-rotating pathers.
Then the physicists compared the turbulence flows in the experiment and the direct numerical simulations to repeated solutions, and it turns out that turbulence accurately tracks one repeated decision after another while the flow remains, and this behavior has already been predicted for low-size chaotic systems, such as the famous Lorenz model.
As a result, the experimental scientists observed recurring decisions to track the chaotic movement in turbulence, but noted that the dynamics of turbulence were much more complex due to the quasi-periodic nature of recurring solutions.
However, they have shown that the organization of turbulence, both in space and over time, is well captured by these structures, and these results will be useful in presenting turbulence in terms of coherent structures and the use of their consistency over time, the aim being to overcome the destructive impact of chaos on the ability of physicists to predict, control and design fluid flows.
What's that gonna mean?
The results of the experiment will affect the community of physicists, mathematicians and engineers who are still trying to understand the turbulence of the liquid, and it is considered to be perhaps the biggest unresolved problem in all science, the authors of the study stress.
Ultimately, the experiment of scientists provides a mathematical basis for the turbulence of the liquid, which is by nature dynamic rather than statistical, so that quantitative projections can be made that are crucial for different applications.
This will not only improve the accuracy of daily weather forecasts, but, most importantly, extreme events such as hurricanes and tornadoes; the dynamic structure is also important for scientists who try to design streams with the required properties; for example, physics can reduce resistance around vehicles to improve fuel efficiency.