**The Concealed Turbulence of Vincent van Gogh’s *The Starry Night***
Vincent van Gogh’s *The Starry Night* (1889) stands as one of the most renowned and acclaimed works in the realm of art. Crafted during his time at an asylum in Saint-Rémy-de-Provence after experiencing a mental crisis, this painting has often been seen as a mirror of the artist’s emotional struggles. The animated night sky, filled with striking blues and energetic brushwork, has enchanted audiences for more than a century. Yet, beyond its emotional depth, new scientific research indicates that *The Starry Night* may serve as an exquisite portrayal of one of nature’s most intricate phenomena: turbulence.
### Van Gogh and Turbulence Science
In physics, turbulence denotes unpredictable and erratic fluid movement, commonly marked by swirling vortices and eddies. This phenomenon can be found in the flow of air, water, and even in the movement of stars. Despite its prevalence in the natural world, turbulence has historically posed significant challenges for physicists seeking to express it mathematically. The Russian physicist Andrei Kolmogorov made notable advancements in the 1940s by uncovering a mathematical correlation, referred to as Kolmogorov scaling, that illustrates how energy flows from larger to smaller eddies within turbulent streams.
Interestingly, van Gogh’s *The Starry Night* seems to encapsulate the core of this intricate phenomenon. A recent study published in *Physics of Fluids* reveals that the swirling motifs in the artwork not only evoke the turbulence of the nocturnal sky but also reveal a second layer of “hidden turbulence” at the microscale, tied to the artist’s brush movements.
### Profound Insight into Natural Events
The research, spearheaded by Yongxiang Huang from Xiamen University in China, posits that van Gogh’s depiction of the swirling night sky signifies a profound, instinctive grasp of natural turbulence. “Van Gogh’s accurate portrayal of turbulence may arise from observing the motion of clouds and the atmosphere, or from an intuitive talent for capturing the dynamic essence of the sky,” Huang remarked.
This isn’t the first occasion scientists have identified a link between van Gogh’s artistry and the principles of turbulence. In a 2014 TED-Ed presentation, Natalya St. Clair, a research associate at the Concord Consortium, utilized *The Starry Night* to illustrate how van Gogh’s methods enabled him to portray the movement of light on water or the flickering of stars. This sparkling effect, she elaborated, results from the human eye’s keen sensitivity to luminance (light intensity) variations, rather than shifts in color.
### The Kolmogorov Link
In 2019, two graduate students from Australia performed a mathematical examination of *The Starry Night* and concluded that the painting possesses turbulent characteristics similar to those found in molecular clouds, where stars originate. Their findings were grounded in a 2004 Hubble image depicting turbulent eddies in dusty clouds around a supergiant star. By analyzing digital images of van Gogh’s artworks, they measured brightness fluctuations between pixels and discovered evidence of Kolmogorov scaling not only in *The Starry Night* but also in two other pieces from that era: *Wheatfield with Crows* and *Road with Cypress and Star* (both created in 1890).
This revelation implies that van Gogh’s portrayal of the night sky closely aligns with the mathematical attributes of turbulence, specifically the energy cascade described by Kolmogorov, wherein larger eddies transmit energy to smaller ones in a self-similar manner across various spatial dimensions.
### Microscale Brushstrokes: Batchelor’s Scaling
Huang and his colleagues advanced this analysis by concentrating on the spatial dimensions of the 14 main vortices in *The Starry Night*. They utilized the relative brightness of the paint colors as a proxy for kinetic energy and assessed the dimensions of van Gogh’s brushstrokes. Their results corroborated the 2019 findings that the painting conforms to Kolmogorov’s law. However, they also identified that at the microscale, the brushstrokes adhere to a different principle known as Batchelor’s scaling.
Batchelor’s scaling, named after Australian mathematician George Batchelor, delineates the smallest-length scales of variations before diffusion prevails in a system. While Kolmogorov’s law pertains to the broader scales of turbulence, Batchelor’s scaling governs the tiniest scales. The presence of both types of scaling within *The Starry Night* is remarkably rare and indicates that van Gogh possessed an extraordinary capacity to encapsulate the full spectrum of turbulent dynamics, from the macroscopic to the microscopic.
### Significance for Fluid Dynamics
The discovery of both Kolmogorov and Batchelor scaling in *The Starry Night* carries implications not only for art history but also for the domain of fluid
