Twenty years ago, two physicists were in a Madrid museum contemplating the work of post-impressionist painter Vincent van Gogh.
One word kept coming back to describe the artist’s work and life: turbulent.
One physicist turned to another to ask: Can we quantify the turbulence in Van Gogh’s paintings?
A new controversy in physics has arisen.
Turbulence is all around us.
It is found in the swirls of the atmosphere that make the flight of an airplane bumpy, the whirlpools that agitate the ocean, the chaotic mixing of gas clouds that contribute to the birth of new stars.
But describing turbulence at a mathematical level is one of the most difficult scientific problems.
Turbulence links the movement of fluids at different scales of a system, feeding energy from large-scale vortices to smaller ones, as a 1922 verse by English mathematician and physicist Lewis Fry Richardson puts it:
“Large eddies have smaller eddies that feed off their velocity, and smaller eddies have lesser eddies and so on down to viscosity.”
In statistical terms, it looks a little different.
In 1941, Andrey N. Kolmogorov, a Soviet mathematician, developed a statistical theory of turbulence.
Kolmogorov’s “scaling law” describes how energy is distributed at different scales in turbulent flow. To measure it in a static painting, the researchers had to devise a method to measure its flow, a problem that held them up for a year. After admiring the emotional turbulence in the museum’s paintings, physicist José Luis Aragón of the National Autonomous University of Mexico and his colleague Manuel Torres of the Spanish National Research Council began looking for mathematical turbulence in some of Van Gogh’s paintings. by examining the differences. in the luminance, or brightness, of pixels separated by a given distance.
They found “Starry Night” to be turbulent, and not just artistically.
A decade later, astrophysicist James Beattie analyzed luminance variations in an area in the middle of the array. He divided the square into three color channels for analysis. He discovered that Van Gogh’s whirlwinds and vortices followed the statistical fluctuations found in another flavor of turbulence that gives rise to the true starry night: supersonic turbulence.
Beattie is an astrophysicist at Princeton University and the Canadian Institute for Theoretical Astrophysics who uses supercomputers to simulate supersonic turbulence and is also captivated by the visual spectacle of turbulence in nature. He recently replaced the sky in Van Gogh’s painting with a simulation of supersonic turbulence.
Yet the question of whether Van Gogh accurately represents turbulence on a mathematical level has not been resolved. Another article appeared, refuting the original article and indicting those who suggested the turmoil was rooted in the work of perpetuating a myth.
Today, a new study published in the journal Physics of Fluids attempts to resolve the question.
Physicist Yongxiang Huang of Xiamen University took the problem to his graduate student, Yinxiang Ma, who began by converting the painting to grayscale.
Then they destroyed the village, the church, the mountains, everything that didn’t flow.
This leaves the 14 swirls in the iconic board.
They began manually analyzing each whorl, measuring several hundred individual brushstrokes, quantifying the brightness and width and length of each stroke.
Beattie notes that in a static painting it is impossible to study the speed or energy of a fluid or gas as scientists typically would.
“Rather, we view the painting itself as a trace of the underlying structure of turbulence,” he said.
In the new study, the researchers discovered classic turbulence in painting: the size of the swirls, their relative distance and intensity followed the physical law discovered by Kolmogorov when they analyzed all the vortices lighting up the night sky, including the moon .
They also found in the variation of brushstrokes a pattern known as Batchelor scaling, named after the Australian mathematician George Batchelor. In 1959, Batchelor identified a universal law describing how a “passive scalar” – which could be a spoonful of cream mixed in coffee, confetti thrown in a turbulent wind, or a jellyfish in ocean currents – is transported by turbulent flow .
What’s unusual, Huang says, is seeing both types of scaling at the same time.
“For many years, scientists have attempted to validate this theory through laboratory experiments and high-resolution numerical simulations using supercomputers,” Huang said. “It is therefore quite surprising to us to observe these two scales in this masterpiece by Van Gogh.”
Huang credits Van Gogh not with understanding the mathematics of turbulence, but as a keen observer of turbulent flows.
“For a turbulence theorist, we pride ourselves on the universality of turbulence: it’s here, it’s there, it’s everywhere. … What I take away from studies like this is that Van Gogh captured some of this universality in the magnificent Starry Night. And I think people know that,” Beattie said in an email. “They know that something wonderful has been incorporated into this painting and we are drawn to it, physicists and laymen alike. Whirlwinds and whirlwinds, they are familiar to us.
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