The midrange wavenumber spectrum of van Gogh’s Starry Night does not obey a turbulent inertial range scaling law

Abstract

ABSTRACTThe swirling night sky painted by van Gogh in his Starry Night painting has been interpreted as a representation of turbulence. Indeed, a popular myth is that this painting quantitatively (albeit coincidentally) captures the scaling behaviour of actual turbulence. One of the most familiar scaling laws in turbulence is the Kolmogorov scaling law, whereby the two-point autocorrelation of the velocity field obeys a −5/3 power law dependence in the midrange (‘inertial range') wavenumbers. Compressible turbulence also obeys a similar power law, but with an exponent between −5/3 and −2, depending on Mach number. An examination of the spectral dependence of a two-point autocorrelation of the image intensity in midrange wavenumbers shows that van Gogh’s Starry Night does obey a power law, but instead with an exponent of −1. Examination of various other van Gogh and impressionist artists’ paintings also do not exhibit the correct power law exponent for a turbulent flow. Thus, van Gogh’s Starry Night painting does not accurately embody one of the most fundamental features of turbulent flows, weakening the foundations of the popular and commonly reiterated myth that this painting captures turbulence in a mathematically correct way.