梵高《星月夜》中的隐藏湍流
Hidden Turbulence in van Gogh's \textbf{\textit{The Starry Night}}
AI总结：
本研究遵循Richardson-Kolmogorov湍流级联图像分析了《星月夜》中所有漩涡，发现其亮度功率谱呈现$-5/3$幂律，揭示了画作中隐藏的湍流物理规律。
摘要：
动荡的天空经常给艺术家带来灵感，尤其是在文森特·梵高的《星月夜》标志性的漩涡中。关于这幅杰作中的流动模式是否遵循Kolmogorov湍流理论，长期以来一直存在激烈的争论。与以往仅考察这幅画作部分内容的研究不同，本工作遵循Richardson-Kolmogorov的湍流级联图像，考虑了画作中所有且仅有的漩涡/涡旋。因此，亮度的傅里叶功率谱自发地呈现出特征性的$-5/3$ Kolmogorov型幂律。这一结果表明，梵高对真实流动进行了非常仔细的观察，使得《星月夜》中漩涡/涡旋的大小及其相对距离和强度都遵循支配湍流的物理定律。此外，在最小漩涡尺度以下的频谱中持续存在“$-1$”型幂律，暗示着具有高施密特数的Batchelor型标量湍流。因此，我们的研究揭示了《星月夜》中捕捉到的隐藏湍流。
英文摘要：
Turbulent skies have often inspired artists, particularly in the iconic swirls of Vincent van Gogh's \textbf{\textit{The Starry Night}}. For an extended period, debate has raged over whether the flow pattern in this masterpiece adheres to Kolmogorov's theory of turbulence. In contrast to previous studies that examined only part of this painting, {\textit{all and only the}} whirls/eddies in the painting are taken into account in this work, following the Richardson-Kolmogorov's cascade picture of turbulence. Consequently, the luminance's Fourier power spectrum spontaneously exhibits a characteristic $-5/3$ Kolmogorov-like power-law. This result suggests that van Gogh had a very careful observation of real flows, so that not only the sizes of whirls/eddies in \textbf{\textit{The Starry Night}} but also their relative distances and intensity follow the physical law that governs turbulent flows. Moreover, a "$-1$"-like power-law persists in the spectrum below the scales of the smallest whirls, hinting at Batchelor-type scalar turbulence with a high Schmidt number. Our study thus unveils the hidden turbulence captured within \textbf{\textit{The Starry Night}}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
