Turbulent scaling law in Ogata Kōrin's Red and White Plum Blossoms

Abstract: Stylized turbulent swirls depicted in artworks are often analyzed with the modern tools for real turbulent flows such as the power spectrum and the structure function. Motivated by the recent study on \textit{The Starry Night} of van Gogh (Ma \textit{et al}., Phys. Fluids, \textbf{36} 095140, 2024), we here analyze Ogata K=orin's \textit{Red and White Plum Blossoms}, in particular its swirling pattern and the bark of the plum-tree trunk. The results show that they follow closely the Obukhov--Corrsin spectrum $k^{-5/3}$ in the inertial-convective range of the passive scalar advected by the homogeneous and isotropic turbulence. Furthermore their 4th- and 6th-order structure functions exhibit approximately the same intermittent scaling law of the passive scalar. We discuss several possible explanations of this consistency.