Tea leaf paradox

The tea leaves collect in the middle and the bottom, instead of along the rim.

In fluid dynamics, the tea leaf paradox is a phenomenon where tea leaves in a cup of tea migrate to the center and bottom of the cup after being stirred rather than being forced to the edges of the cup, as would be expected in a spiral centrifuge.

The correct physical explanation of the paradox was for the first time given by James Thomson in 1857. He correctly connected the appearance of secondary flow (both Earth atmosphere and tea cup) with ″friction on the bottom″.^[2] The formation of secondary flows in an annular channel was theoretically treated by Joseph Valentin Boussinesq as early as in 1868.^[3] The migration of near-bottom particles in river-bend flows was experimentally investigated by A. Ya. Milovich in 1913.^[1] The solution first came from Albert Einstein in a 1926 paper in which he explained the erosion of river banks, and repudiated Baer's law.^[4]^[5]

^ ^a ^b His results are cited in: Joukovsky N.E. (1914). "On the motion of water at a turn of a river". Matematicheskii Sbornik. 29. Reprinted in: Collected works. Vol. 4. Moscow; Leningrad. 1937. pp. 193–216, 231–233 (abstract in English).{{cite book}}: CS1 maint: location missing publisher (link)
^ James Thomson, On the grand currents of atmospheric circulation (1857). Collected Papers in Physics and Engineering, Cambridge Univ., 1912, 144-148 djvu file
^ Boussinesq J. (1868). "Mémoire sur l'influence des frottements dans les mouvements réguliers des fluides" (PDF). Journal de mathématiques pures et appliquées. 2e Série. 13: 377–424. Archived from the original (PDF) on March 17, 2022.
^ Bowker, Kent A. (1988). "Albert Einstein and Meandering Rivers". Earth Science History. 1 (1): 45. Bibcode:1988ESHis...7...45B. doi:10.17704/eshi.7.1.yk72n55q84qxu5n6. Retrieved 2008-12-28.
^ Einstein, Albert (March 1926). "Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes". Die Naturwissenschaften. 14 (11). Berlin / Heidelberg: Springer: 223–4. Bibcode:1926NW.....14..223E. doi:10.1007/BF01510300. S2CID 39899416. English translation: The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer's Law, accessed 2017-12-12.

[Joukovsky-1] His results are cited in: Joukovsky N.E. (1914). "On the motion of water at a turn of a river". Matematicheskii Sbornik. 29. Reprinted in: Collected works. Vol. 4. Moscow; Leningrad. 1937. pp. 193–216, 231–233 (abstract in English).{{cite book}}: CS1 maint: location missing publisher (link)

[2] James Thomson, On the grand currents of atmospheric circulation (1857). Collected Papers in Physics and Engineering, Cambridge Univ., 1912, 144-148 djvu file

[3] Boussinesq J. (1868). "Mémoire sur l'influence des frottements dans les mouvements réguliers des fluides" (PDF). Journal de mathématiques pures et appliquées. 2e Série. 13: 377–424. Archived from the original (PDF) on March 17, 2022.

[4] Bowker, Kent A. (1988). "Albert Einstein and Meandering Rivers". Earth Science History. 1 (1): 45. Bibcode:1988ESHis...7...45B. doi:10.17704/eshi.7.1.yk72n55q84qxu5n6. Retrieved 2008-12-28.

[Naturwissenschaften-5] Einstein, Albert (March 1926). "Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes". Die Naturwissenschaften. 14 (11). Berlin / Heidelberg: Springer: 223–4. Bibcode:1926NW.....14..223E. doi:10.1007/BF01510300. S2CID 39899416. English translation: The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer's Law, accessed 2017-12-12.

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