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I was watching the rainbow today and started thinking about the effects of the rain falling in different directions.

The idea I had was that normally we model rain drops as small spheres, and this gives a characterizing angle for the perceived rainbow.

Now, if the rain falls with a large horizontal velocity component, will this deform the raindrops, making them more elliptic, thus changing the angle of the perceived rainbow?

Or formulated in other words: Can one determine the speed of the falling rain from the angle of the rainbow?

PS: I know there could also be a minuscule relativistic effect here, due to length contraction, but for this particular question I'm not considering relativistic rain.

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    $\begingroup$ Why do you suppose that horizontal forces deform raindrops but vertical forces don't? In reality, raindrops are neither spherical, nor ellipsoidal (nor teardrop-shaped). $\endgroup$ – David Richerby Sep 4 '17 at 9:13
  • $\begingroup$ There are a lot of things about rain i don't know, but one has to start somewhere right? In the spirit of the question it doesn't really matter what the "normal" shape of the raindrop is, only if is changes under vertical forces. $\endgroup$ – Mikael Fremling Sep 4 '17 at 9:23
  • $\begingroup$ Sure. It just seems strange to assume that forces in one direction cause distortion, while forces in another don't. The link to the actual shape was intended as an "oh, by the way." I'm sorry I forgot to include any wording to suggest that. $\endgroup$ – David Richerby Sep 4 '17 at 9:33
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There is a theory of rainbows due to elliptical droplets. It was started by Willy Möbius [1] but is perhaps more clearly described in the modern papers [2,3]. Unfortunately the math is messy. While this may change the appearance of the rainbow, the biggest effect is on the angles between the different order rainbows: by measuring them one can presumably work backwards and get a value of the ellipticity.

Except for one problem: raindrops made ellipsoidal because of wind oscillate (they are water after all). They will hence change their ellipticity rapidly; to make matters worse, the degree of maximal ellipticity change scales roughly parabolically with droplet size and droplets can become non-ellipsoidal [4,5,6]. Hence a real rainstorm (with different droplet sizes and vibration modes) will produce a rather messy signal.

So the answer to your question is likely "yes, for rigid uniform droplets" and "no, not for real rain".


Citations:

[1] Möbius, W. (1910). Zur Theorie des Regenbogens und ihrer experimentellen Prüfung. Annalen der Physik, 338(16), 1493-1558.

[2] Lock, J. A., & Können, G. P. (2017). Rainbows by elliptically deformed drops. I. Möbius shift for high-order rainbows. Applied Optics, 56(19), G88-G97. http://www.guntherkonnen.com/articles/322

[3] Können, G. P., & Lock, J. A. (2017). Rainbows by elliptically deformed drops. II. The appearance of supernumeraries of high-order rainbows in rain showers. Applied Optics, 56(19), G98-G103. http://www.guntherkonnen.com/articles/323

[4] Szakáll, M., Mitra, S. K., Diehl, K., & Borrmann, S. (2010). Shapes and oscillations of falling raindrops—A review. Atmospheric research, 97(4), 416-425. http://e-science.sources.ru/sites/default/files/upload_forums_files/y0/sdarticle2.pdf

[5] Thurai, M., Bringi, V. N., Manić, A. B., Šekeljić, N. J., & Notaroš, B. M. (2014). Investigating raindrop shapes, oscillation modes, and implications for radio wave propagation. Radio Science, 49(10), 921-932.

[6] https://www.joanneum.at/uploads/tx_publicationlibrary/img494.pdf

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