Long before equations described it, Van Gogh's linseed oil and stone pigments depicted the turbulence behind twinkling stars. Credit: Museum of Modern Art/Google Arts & Culture/Wikimedia Commons
Turbulence abounds in nature, from the swirling eddies of hurricanes to the bright swirls of Jupiter’s immense storms. Astronomers have even observed it where stars are born in the vast maelstrom of molecular clouds. But try as scientists might, no theory has managed to capture the full scale and unpredictability of turbulence. Nobel laureate Richard Feynman once called it “the most important unsolved problem in classical physics.”
However, a study published today in Fluid physics Artist Vincent van Gogh captured theories of fluid dynamics in “The Starry Night,” which shows complex patterns of turbulence on large and small scales. Scientists say the revered oil-on-canvas work, painted in June 1889, captures details that adhere with astonishing fidelity to the physical laws of turbulence — laws that would not be formulated until 52 years later.
Turbulence in the atmosphere triggers the phenomenon astronomers call vision: When light passes through swirling air, it refracts, causing images to blur and stars to vibrate with brilliance. In other words, whether by supernatural intuition or meticulous observation, Van Gogh’s dynamic depiction of swirls and starlight captured the very physics that makes air swirl and stars twinkle.
Ironically, Van Gogh considered The Starry Night to be a failure. To save shipping costs, he decided not to send it along with other paintings to his brother Theo, an art dealer, for sale to the public. Today it is one of the most recognized and acclaimed paintings in Western art.
It has also become a matter of considerable scientific interest. last 16 yearsFluid dynamicists have debated in research papers whether “The Starry Night” truly reflects the mathematical structure of turbulence or, like many other works (including Edvard Munch’s “The Scream”), simply imitates it.
“Our findings resolve the ongoing debate over whether the dynamic sky in this famous painting reflects real physical phenomena,” says study co-author Yongxiang Huang of Xiamen University in China.
The leading role of art
Created a year before Van Gogh’s death, when the artist was in a mental asylum in France, “The Starry Night” depicts large, twinkling stars and a crescent moon amid a chaotic, swirling blue sky. Like many Impressionist paintings of the period, it uses “broken colors,” the technique of placing different colors next to others that appear equally bright, creating a dramatic, pulsating effect of fluidity and movement.
At that time, scientific understanding of turbulence was very limited. It was not until half a century later that the Russian physicist Andrey Kolmogorov formulated the first equations to describe turbulence.
Kolmogorov described how energy cascades from large eddies to smaller eddies, a phenomenon that can be observed in nature. For example, in low-resolution images, Jupiter's Great Red Spot appears to be a single large eddy. But if you zoom in, you see smaller and smaller eddies feeding off the energy of larger ones.
Huang and his colleagues analyzed the 14 major swirls in “The Starry Night.” Unlike previous teams that also looked for turbulence in “The Starry Night,” they focused only on the swirls, blocking out the rest of the sky. They then measured the brightness variations in each of them to see if they matched those predicted by theory.
Remarkably, Van Gogh passes with flying colors. The Kolmogorov equation predicts that energy falls through different eddy sizes in the form of an inverse power law with an exponent of -5/3, or -1.67 in rounded decimal form. The new work finds that the eddies in “The Starry Night” obey this law with remarkable precision, with an exponent of -1.67 or -1.68 (depending on whether measured from top to bottom or from top to bottom), with associated uncertainties of 0.13 and 0.19.
In “The Starry Night” and its dynamic sky, “the arrangement of the swirling formations created by van Gogh resembles the mechanism of energy transfer in real turbulent flows,” the authors write.
Science imitates art
Because turbulence has eluded mathematical description for so long, physicists throughout history have admired artists’ ability to capture its appearance in nature. In fact, the first use of the word “turbulence” applied to fluid flow appears in the writings of Leonardo da Vinci, who conducted painstaking studies of water flow.
However, on closer inspection, many works of art depicting turbulence do not correspond to the scale predicted by Kolmogorov. These include Da Vinci's water sketches, as well as Edvard Munch's “The Scream,” with its undulating, restless sky.
In addition to the Kolmogorov-like turbulent structures that Van Gogh depicts in “The Starry Night,” the new study finds that another aspect of turbulence is depicted in the painting. The team found that at smaller scales (comparable to the width of a brushstroke), “The Starry Night” corresponds precisely to a different scaling relationship formulated by Australian mathematician George Batchelor, with an exponent of -1.
While the Kolmogorov equation defines how energy is distributed across eddies, the Batchelor relation describes how turbulence mixes a fluid at smaller scales. (This mixing can be visualized by releasing a dye or paint into a turbulent flow.) The team says the appearance of the Batchelor scale in “The Starry Night” is related to the mixing of the paint itself — linseed oil and stone pigment carried across the canvas by Van Gogh’s rapid brushstrokes.
“The most exciting aspect of our study is the simultaneous observation of the Kolmogorov and Batchelor scales,” Huang says.
Fluid dynamicists have long sought to simultaneously observe the Kolmogorov and Batchelor scales in laboratory experiments. This is difficult, Huang says, because it involves observing very large-scale and very small-scale structures at the same time. But the fact that both can be observed in a work of art could inspire new approaches to laboratory experiments, the authors write.
