The starlight and swirling clouds of Vincent van Gogh’s Starry Night are thought to reflect the artist’s turbulent state of mind when he painted the work in 1889. Analysis of Chinese and French physicists indicates that the artist had a deep intuitive understanding of the mathematical structure of turbulence.
As a common natural phenomenon observed in liquids and gases – water eddies, ocean currents, blood flow, storm clouds and cigarette or chimney smoke – turbulent flow is chaotic, because in addition to the mean flow velocity, each liquid or gas particle has an additional speed that can be partly in the direction of the main flow, partly against the direction of the flow.
To the casual observer this phenomenon may seem random, but turbulence nevertheless follows a cascading pattern that can be studied and, at least partially, explained by mathematical equations.
Photo by Žan Koroli
“Imagine standing on a bridge and watching the river flow. You will see eddies on the surface, and these eddies are not random. They arrange themselves into specific patterns, and these types of patterns can be predicted by physical laws,” said Yongxiang Huang, lead author of the study, which was published in the scientific journal Fizika fluida (Physics of Fluids). Huang is a researcher at the State Laboratory at Xiamen University in Southeast China.
Van Gogh oil on canvas Starry nightas noted in the study, depicts the sky just before sunrise from the east-facing window of the artist’s room in Saint-Rémy, southern France, where the artist was housed after cutting off his left ear.
The researchers studied 14 vortices, or swirls, in Van Gogh’s celebrated painting.
After digitizing the image, Huang and his colleagues studied the scale of its 14 main vortex shapes to see if they were consistent with physical theories that describe the transfer of energy from large vortices to small ones as they collide and interact with each other.
Starry night and theories of turbulence
The atmospheric movement of a painted sky cannot be directly measured, so Huang and his colleagues precisely measured the brushstrokes and compared the size of the strokes to the mathematical scales of turbulence theories. To assess physical movement, they used relative luminance or the luminance of different color tones.
They found that the size of 14 vortices in Starry night and their relative distance and intensity follow the physical law governing fluid dynamics known as Kolmogorov theory of turbulence.
During the 1940s, the Soviet mathematician Andrei Kolmogorov described a mathematical connection between fluctuations in the flow rate and the rate at which its energy is dissipated.
The researchers analyzed the brushstrokes and compared them with mathematical calculations
Huang and his team also found that the color, at the smallest scale, mixes with some background eddies and eddies in a way predicted by turbulence theory, following a statistical pattern known as Batchelor scaling. Batchelor scaling mathematically represents how small particles, such as algae floating in the ocean or dust particles in the wind, passively mix with the turbulent flow.
“This is cool. Indeed, these are the kinds of statistics you would expect from ocean currents or dust and airborne particles,” James Beatty, a postdoctoral fellow in the Department of Astrophysics at Princeton University in New Jersey, told Yes-In-In. Bitti was not involved in the aforementioned study, but was engaged in similar research on works of art.
“In my research, I really only studied large vortices in the images, so I didn’t notice this second relation,” he adds, referring to Batchelor’s scaling.
‘Incredible Coincidence’
Of course, Huang said, Van Gogh was certainly not versed in mathematical equations, but he probably spent a lot of time observing turbulence in nature.
“I think this physical connection must have been embedded in his mind, and hence this famous image, Starry nightmimics the real flow,” Huang points out.
Bitti agrees. “It is an amazing coincidence that Van Gogh’s beautiful painting coincides with the formulas of turbulence.”
“This makes some sense – the models are constructed in an attempt to understand the statistics of eddies and turbulence at multiple scales, where each eddy interacts with the others through a turbulent cascade. In a sense, Van Gogh painted something that represents this phenomenon, so why shouldn’t there be a convergence between the theoretical models and the statistics of Van Gogh’s vortices?”
The research team performed the same analysis and discovered the same phenomenon in two other images, in one image, Port of Brightonmade by the British artist John Constable in 1826-7, and in the second photo of Jupiter’s Great Red Spot, taken by NASA’s Voyager spacecraft on March 15, 1979.
Turbulence on Jupiter
“Unlike Starry nightsthis image lacks well-defined swirling patterns, but the clouds are rich in structures of various scales, reminiscent of those often seen in the sky,” according to a study of Constable’s artwork.
In an exhibition at the Museum of Modern Art in New York, Starry night is an extremely popular piece of art that has been reproduced from Legos, drones and dominoes.
The mystery of physics
Huang notes that scientists have long struggled to describe turbulent flow in fluid dynamics in a way that would allow them to predict the phenomenon, and that a complete explanation remains the prevailing mystery of physics. A thorough understanding would help in weather forecasting, turbulence during flight and many other processes, the scientist points out.
One of the examples of turbulence flow
“Even after more than 100 years of study, we don’t even know how to define this complex phenomenon,” emphasizes Huang. “It’s extremely important, but it’s extremely difficult.”
The fact that Starry night matching statistical models of turbulence even though the artwork does not actually move may indicate that statistical methods and tools are less precise than scientists may have thought, says Biti. The image cannot be precisely measured because “It’s not actually turbulence. There is no kinetic energy.”
However, Beatty emphasizes that he is a big fan of this artwork and that it reflects the universality and beauty of turbulence.
“What can be concluded from such studies is that Van Gogh captured part of this universality in his Starry night. And I think people know that. They know that something wonderful is embedded in this picture and that attracts us”, concludes Biti.
Source: www.sitoireseto.com
