Hidden Turbulence in van Gogh's \textbf{\textit{The Starry Night}}

TL;DR

This study reveals that Vincent van Gogh's The Starry Night depicts a pattern of turbulence consistent with physical turbulence laws, suggesting careful observation of real flows and uncovering hidden turbulence in the painting.

Contribution

The paper demonstrates that the luminance pattern in The Starry Night follows Kolmogorov turbulence laws, linking art analysis with fluid dynamics.

Findings

Fourier spectrum exhibits -5/3 power-law consistent with Kolmogorov turbulence

Presence of -1-like power-law indicating Batchelor-type scalar turbulence

All whirl/eddy scales and their relations follow physical turbulence laws

Abstract

Turbulent skies have often inspired artists, particularly in the iconic swirls of Vincent van Gogh's \textbf{\textit{The Starry Night}}. For an extended period, debate has raged over whether the flow pattern in this masterpiece adheres to Kolmogorov's theory of turbulence. In contrast to previous studies that examined only part of this painting, {\textit{all and only the}} whirls/eddies in the painting are taken into account in this work, following the Richardson-Kolmogorov's cascade picture of turbulence. Consequently, the luminance's Fourier power spectrum spontaneously exhibits a characteristic $-5/3$ Kolmogorov-like power-law. This result suggests that van Gogh had a very careful observation of real flows, so that not only the sizes of whirls/eddies in \textbf{\textit{The Starry Night}} but also their relative distances and intensity follow the physical law that governs turbulent flows. Moreover, a "$-1$"-like power-law persists in the spectrum below the scales of the smallest whirls, hinting at Batchelor-type scalar turbulence with a high Schmidt number. Our study thus unveils the hidden turbulence captured within \textbf{\textit{The Starry Night}}.