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 $\mathcal{P}(k)\propto k^{-2.1\pm 0.3}$ in the scaling range, $34\le k\le 80$. We identify a driving scale, $k_{\text{D}}=3$, dissipation scale, $k_{\nu }=220$ 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.

arXiv comment6 pages, 4 figures