Fysikere afslører nye dynamiske rammer for turbulens

Turbulens spiller en nøglerolle i vores daglige liv, hvilket giver ujævne flyveture, påvirker vejr og klima, begrænser brændstofeffektiviteten af ​​de biler, vi kører, og påvirker ren energiteknologi. Alligevel har videnskabsmænd og ingeniører undret sig over måder at forudsige og ændre turbulente væskestrømme, og det har længe været et af de mest udfordrende problemer inden for videnskab og teknik.

Nu har fysikere fra Georgia Institute of Technology påvist – numerisk og eksperimentelt – at turbulens kan forstås og kvantificeres ved hjælp af et relativt lille sæt specielle løsninger til de styrende ligninger for væskedynamik, der kan forudberegnes for en bestemt geometri, én gang for alle.

"I næsten et århundrede er turbulens blevet beskrevet statistisk som en tilfældig proces," sagde Roman Grigoriev. "Vores resultater giver den første eksperimentelle illustration af, at turbulensens dynamik på passende korte tidsskalaer er deterministisk - og forbinder den med de underliggende deterministiske styrende ligninger."

Resultaterne blev offentliggjort i Proceedings of the National Academy of Sciences den 19. august 2022. Holdet af forskere blev ledet af Grigoriev og Michael Schatz, professorer ved School of Physics ved Georgia Tech, som har samarbejdet om forskellige forskningsprojekter i løbet af de sidste to årtier.

Schatz og Grigoriev fik følgeskab i studiet af School of Physics kandidatstuderende Chris Crowley, Joshua Pughe-Sanford og Wesley Toler sammen med Michael Krygier, en postdoc ved Sandia National Laboratories, som udviklede undersøgelsens numeriske løsere som kandidatstuderende på Georgia Tech.

En ny 'køreplan' for turbulensforskning

Kvantitativt at forudsige udviklingen af ​​turbulente strømme - og faktisk næsten alle deres egenskaber - er ret vanskeligt. "Numerisk simulering er den eneste pålidelige eksisterende forudsigelsestilgang," sagde Grigoriev. "Men det kan være forfærdeligt dyrt. Målet med vores forskning var at gøre forudsigelse billigere."

Forskerne skabte en ny "køreplan" for turbulens ved at se på en svag turbulent strømning, der var indespærret mellem to uafhængigt roterende cylindre - hvilket giver holdet en unik måde at sammenligne eksperimentelle observationer med numerisk beregnede strømme på grund af fraværet af "sluteffekter" der er til stede i mere velkendte geometrier, såsom strømning ned i et rør.

"Turbulens kan opfattes som en bil, der følger en række veje," sagde Grigoriev. "Måske en endnu bedre analogi er et tog, som ikke kun følger en jernbane efter en foreskreven køreplan, men også har samme form som den jernbane, det følger."

Eksperimentet indeholdt gennemsigtige vægge for at give fuld visuel adgang, og det brugte en state-of-the-art flowvisualisering for at give forskerne mulighed for at rekonstruere flowet ved at spore bevægelsen af ​​millioner af suspenderede fluorescerende partikler. In parallel, advanced numerical methods were used to compute recurrent solutions of the partial differential equation (Navier-Stokes equation), governing fluid flows under conditions exactly matching experiment.

It is well-known that turbulent fluid flows exhibit a repertoire of patterns—referred to as "coherent structures" in the field—that have a well-defined spatial profile but appear and disappear in an apparently random manner. By analyzing their experimental and numerical data, the researchers discovered that these flow patterns and their evolution resemble those described by the special solutions they computed. These special solutions are both recurrent and unstable, meaning they describe repeating flow patterns over short intervals of time. Turbulence tracks one such solution after another, which explains what patterns can appear, and in what order.

Recurrent solutions, two frequencies

"All the recurrent solutions that we found in this geometry turned out to be quasi-periodic—that is, characterized by two different frequencies," said Grigoriev. One frequency described the overall rotation of the flow pattern around the axis of symmetry of the flow, while the other described the changes in the shape of the flow pattern in a reference frame co-rotating with the pattern. The corresponding flows repeat periodically in these co-rotating frames.

"We then compared turbulent flows in experiment and direct numerical simulations with these recurrent solutions and found turbulence to closely follow (track) one recurrent solution after another, for as long as turbulent flow persisted," Grigoriev said. "Such qualitative behaviors were predicted for low-dimensional chaotic systems, such as the famous Lorenz model, derived six decades ago as a greatly simplified model of the atmosphere."

The work represents the first experimental observation of chaotic motion tracking recurrent solutions actually observed in turbulent flows. "The dynamics of turbulent flows are, of course, far more complicated due to the quasi-periodic nature of recurrent solutions," Grigoriev added.

"Using this method, we conclusively showed 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 leveraging their persistence in time to overcome the devastating effects of chaos on our ability to predict, control, and engineer fluid flows."

A new dynamical foundation for 3D fluid flows

These findings most immediately impact the community of physicists, mathematicians, and engineers who are still trying to understand fluid turbulence, which remains "perhaps the greatest unsolved problem in all of science," Grigoriev said.

"This work builds and expands on previous work on fluid turbulence by the same group, some of which was reported at Georgia Tech in 2017," he added. "Unlike the work discussed in that publication, which focused on idealized two-dimensional fluid flows, present research addresses the practically important and more complicated three-dimensional flows."

Ultimately, the team's study lays a mathematical foundation for fluid turbulence which is dynamical, rather than statistical, in nature—and hence has the capability to make quantitative predictions, which are crucial for a variety of applications.

"It can give us the ability to dramatically improve the 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." + Udforsk yderligere

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