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I read about turbulence a few days back.I saw a video showing the physics behind van gogh's starry night and physics.But I could not really understand the link between starry night and physics of turbulence.Please explain.

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    $\begingroup$ This seems to be fairly broad $\endgroup$
    – Kyle Kanos
    Commented Apr 23, 2015 at 17:42
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    $\begingroup$ van Gogh painted it at a turbulent point in his life $\endgroup$
    – pentane
    Commented Apr 23, 2015 at 18:28

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I saw the same article and was not impressed. The author seemed to imply that Van Gough was using the shape of vorticies shedding off of a cylindrical cross section in a moving fluid as the basis for the shape of the stars in his painting. Even if there had been some scientific observation of vortex shedding (and there may well have been) at that time, there wouldn't be any physical connection between that phenomenon and the appearance of stars in the night sky.

I've also read (reference needed) that some of his paintings may have reflected what his vision was like as a result of either medication he was on, or as a result of his mental illness. That seems more likely to me (unsubstantiated opinion!).

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OKay, so I read this question and thought "There's no darn way that they mean 'turbulence' in the scientific sense!" But then I did a quick literature search and found Turbulent Luminance in Impassioned van Gogh Paintings.

In the paper, they compare the probability density function (PDF) of four paintings from the same era of van Gogh's life to the theoretical distributions hypothesized by Kolmogorov. : Starry Night, Wheat Field with Crows, Two Peasant Women Digging in Field with Snow and Road with Cypress and Star. To do this, the authors computed autocorrelation functions of the luminance between pixels in the images across the entire paintings.

Here is the first thing to note -- although these paintings "look like turbulence," the authors are measuring the luminance and comparing to turbulence, not comparing the vortices shape/size/etc! The luminance is defined to be a scalar intensity of the color at each red-green-blue (RGB) pixel:

$$L = 0.299 R + 0.587 G + 0.114B $$

I cannot reproduce their figures here for copyright reasons, but it's definitely something worth seeing. The results from all of the paintings match very well with the theoretical distributions for velocity fluctuations. Which I was certainly surprised to see.

So, while I haven't seen the video to which you refer, it sounds like it took a grain of truth and misrepresented it. The structures/eddies/vortices in Starry Night are not turbulent structures. However, the luminance in the painting, and in several others, actually has the same characteristics as a turbulent flow.

I'll close with the conclusions from the paper directly quoted:

In summary, our results show that Starry Night , and other impassioned van Gogh paintings, painted during periods of prolonged psychotic agitation transmitted the essence of turbulence with high realism. We use digital images of these paintings to show that the statistics of luminance contains the characteristic fingerprint of turbulent flow, according to a mathematical theory of turbulence based on the statistical approach developed by A. Kolmogorov. The analysis of the luminance of a painting presented here may be a useful tool for the relatively new field of using quantitative objective research for analyzing artwork.

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