Vincent van Gogh’s most famous painting Starry Night (1889) was created (along with several other masterpieces) by the artist during his stay in a psychiatric hospital in Arles after he became insane in December 1888. Starry Night Physicists often see it as a masterful depiction of atmospheric turbulence, reflecting Van Gogh’s own inner conflict. New Paper A study published in the journal Physics of Fluids says the appearance of movement in Van Gogh’s blue sky is due to a second kind of “hidden turbulence” at the microscopic level that permeates the size of the paint strokes – the entire canvas.
“It reveals a deep, intuitive understanding of natural phenomena.” Co-author Huang Yongxiang said: “Van Gogh’s precise depiction of turbulence may have been due to his studies of cloud and atmospheric movement, or perhaps to his innate sense for capturing the dynamism of the sky,” said Professor Van Gogh of Xiamen University in China.
As previously reported, 2014 TED-Ed TalkNatalia St. Claire, Research Fellow He is a co-author of the Concord Consortium. The Art of Mental ArithmeticUsed Starry Night To clarify the concept of turbulence in a moving fluid, she said Van Gogh’s technique allowed him to depict the movement of light across the surface of water or the twinkling of stars, which we see as a kind of shimmering effect because our eyes are sensitive to changes in the intensity of light (this property is called “turbulence”). brightness) is more important than the color change.
In physics, turbulence is associated with strong, sudden motions in air or water, usually characterized by eddies and whirlpools. Physicists have been trying for centuries to mathematically describe turbulence, which remains one of the great challenges in the field. However, Russian physicist Andrey Kolmogorov A major breakthrough came in the 1940s when he predicted that there was a mathematical relationship (now known as Kolmogorov scaling) between how the speed of a flow varies with time and the rate at which energy is lost due to friction.
That is, some turbulence exhibits energy cascades, where larger eddies transfer some of their energy to smaller eddies, which in turn transfer some of their energy to even smaller eddies, and so on, producing self-similar patterns at many spatial size scales. Subsequent experimental evidence has shown that Kolmogorov’s predictions were not far off the mark.
In 2019, two Australian graduate students Mathematically analyzed They concluded that this painting has the same turbulent characteristics as molecular clouds (where stars are literally born). 2004 Hubble image It’s an observation of turbulent eddies in a cloud of dust moving around a supergiant star.The researchers looked at several digital photos of Van Gogh’s paintings, measured the difference in brightness between any two pixels, and calculated the probability that two pixels at a certain distance will have the same brightness. They found evidence Something very close to Kolmogorov scaling, Starry Nightand similar representations can be found in two other paintings from the same period in Van Gogh’s life. Wheat field with crows and Cypress and star trail (Both painted in 1890).
Micro-scale brushwork
Huang is a marine scientist who collaborated with physicists to delve into the turbulence patterns in Van Gogh’s masterpiece. They focused on studying the spatial scale of the painting’s 14 major vortices, using the relative brightness of the paint colors as an analogy for kinetic energy. Specifically, they precisely measured the size of typical brushstrokes and compared the scale to what fluid dynamics would predict.
Their findings confirmed a 2019 conclusion that the painting as a whole roughly follows Kolmogorov’s law. The team also found that at the microscopic scale, the paint strokes ” Scaling the BachelorNamed after an Australian mathematician George Batchelorwho specializes in fluid mechanics. It is similar to Kolmogorov’s law, but describes the smallest scale of turbulence before viscosity becomes dominant in a system, whereas Batchelor scaling describes the smallest length scale of fluctuations before diffusion becomes dominant. According to the authors, it is very rare to find both types of scaling in one atmospheric system.
This is further evidence that Van Gogh had a keen instinct for chaos and expressed it beautifully. Starry NightThere may also be implications for fluid mechanics: “Turbulence is considered to be one of the essential properties of inertia-dominated high Reynolds number flows, but recently turbulence-like phenomena have been reported at viscosity-dominated low Reynolds numbers and in different types of flow systems over a wide range of spatial scales.” Huang says“It seems time to propose a new definition of turbulence to accommodate more situations.”
Fluid Physics, 2024. DOI: 10.1063/5.0213627 (About DOIs)