A September 17, 2024 American Institute of Physics news release (also on EurekAlert) reveals how researchers in the fields of marine sciences and fluid dynamics have revealed the ‘hidden turbulence’ in van Gogh’s The Starry Night,

Vincent van Gogh’s painting “The Starry Night” depicts a swirling blue sky with yellow moon and stars. The sky is an explosion of colors and shapes, each star encapsulated in ripples of yellow, gleaming with light like reflections on water. 

Van Gogh’s brushstrokes create an illusion of sky movement so convincing it led atmospheric scientists to wonder how closely it aligns with the physics of real skies. While the atmospheric motion in the painting cannot be measured, the brushstrokes can.

In an article published this week in Physics of Fluids, by AIP Publishing, researchers specializing in marine sciences and fluid dynamics in China and France analyzed van Gogh’s painting to uncover what they call the hidden turbulence in the painter’s depiction of the sky.

“The scale of the paint strokes played a crucial role,” author Yongxiang Huang said. “With a high-resolution digital picture, we were able to measure precisely the typical size of the brushstrokes and compare these to the scales expected from turbulence theories.”

To reveal hidden turbulence, the authors used brushstrokes in the painting like leaves swirling in a funnel of wind to examine the shape, energy, and scaling of atmospheric characteristics of the otherwise invisible atmosphere. They used the relative brightness, or luminance, of the varying paint colors as a stand-in for the kinetic energy of physical movement.

“It reveals a deep and intuitive understanding of natural phenomena,” Huang said. “Van Gogh’s precise representation of turbulence might be from studying the movement of clouds and the atmosphere or an innate sense of how to capture the dynamism of the sky.”

Their study examined the spatial scale of the painting’s 14 main whirling shapes to find out if they align with the cascading energy theory that describes the kinetic energy transfer from large- to small-scale turbulent flows in the atmosphere.

They discovered the overall picture aligns with Kolmogorov’s law, which predicts atmospheric movement and scale according to measured inertial energy. Drilling down to the microcosm within the paint strokes themselves, where relative brightness is diffused throughout the canvas, the researchers discovered an alignment with Batchelor’s scaling, which describes energy laws in small-scale, passive scalar turbulence following atmospheric movement.

Finding both scalings in one atmospheric system is rare, and it was a big driver for their research.

“Turbulence is believed to be one of the intrinsic properties of high Reynolds flows dominated by inertia, but recently, turbulence-like phenomena have been reported for different types of flow systems at a wide range of spatial scales, with low Reynolds numbers where viscosity is more dominant,” Huang said.

“It seems it is time to propose a new definition of turbulence to embrace more situations.”

Matthew Rozsa provides a more accessible description of the research in a September 20, 2024 article for Salon.com, Note: Links have been removed,

… one can look at “The Starry Night” and see a scientifically accurate representation of turbulent, cascading waters — a visual that may have directly inspired van Gogh before he transposed those dynamics into his iconic starry sky while painting in his mental asylum room in the French town of Saint-Rémy-de-Provence.

“Imagine you are standing on a bridge, and you watch the river flow. You will see swirls on the surface, and these swirls are not random.” Yongxiang Huang, lead author of the study, told CNN. “They arrange themselves in specific patterns, and these kinds of patterns can be predicted by physical laws.”

Scientists fascinated by van Gogh’s art are not limited to physicists. When researchers discovered a gecko that reminded them of the paintings of van Gogh, they gave it the scientific name Cnemaspis vangoghi. As a common terms, the authors suggested “van Gogh’s starry dwarf gecko.”

Here’s a link to and a citation for the paper,

Hidden turbulence in van Gogh’s The Starry Night by Yinxiang Ma (马寅翔), Wanting Cheng (程婉婷), Shidi Huang (黄仕迪), François G. Schmitt, Xin Lin (林昕), Yongxiang Huang (黄永祥). Physics of Fluids Volume 36, Issue 9 September 2024 DOI: https://doi.org/10.1063/5.0213627

This article is behind a paywall.