Is The Starry Night Turbulent?

Abstract

Vincent van Gogh's painting, The Starry Night, is an iconic piece of art and cultural history. The painting portrays a night sky full of stars, with eddies (spirals) both large and small. \cite{Kolmogorov1941}'s description of subsonic, incompressible turbulence gives a model for turbulence that involves eddies interacting on many length scales, and so the question has been asked: is The Starry Night turbulent? To answer this question, we calculate the azimuthally averaged power spectrum of a square region ($1165 \times 1165$ pixels) of night sky in The Starry Night. We find a power spectrum, $\mathcal{P}(k)$, where $k$ is the wavevector, that shares the same features as supersonic turbulence. It has a power-law $\mathcal{P}(k) \propto k^{-2.1\pm0.3}$ in the scaling range, $34 \leq k \leq 80$. We identify a driving scale, $k_\text{D} = 3$, dissipation scale, $k_ν= 220$ and a bottleneck. This leads us to believe that van Gogh's depiction of the starry night closely resembles the turbulence found in real molecular clouds, the birthplace of stars in the Universe.