Hidden turbulence in van Gogh's The Starry Night

Abstract

Turbulent skies have often inspired artists, particularly in the iconic swirls of Vincent van Gogh's 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, 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 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 The Starry Night.