Turbulent scaling law in Ogata K\=orin's Red and White Plum Blossoms

TL;DR

This paper analyzes the swirling patterns in Ogata Kōrin's artwork, revealing they follow turbulence scaling laws similar to those in fluid dynamics, suggesting a connection between art and turbulent flow physics.

Contribution

It demonstrates that artistic swirling patterns can be quantitatively described by turbulence scaling laws, bridging art analysis and fluid turbulence theory.

Findings

Swirling patterns follow the Obukhov--Corrsin spectrum $k^{-5/3}$.

Higher-order structure functions exhibit similar intermittent scaling.

Artistic patterns show characteristics of passive scalar turbulence.

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.