Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Reynolds' Turbulence Solution

Version 1 : Received: 10 August 2019 / Approved: 12 August 2019 / Online: 12 August 2019 (05:39:11 CEST)
Version 2 : Received: 29 October 2019 / Approved: 30 October 2019 / Online: 30 October 2019 (04:49:17 CET)
Version 3 : Received: 1 December 2021 / Approved: 3 December 2021 / Online: 3 December 2021 (10:16:34 CET)

A peer-reviewed article of this Preprint also exists.

Sun, Bohua. "Revisiting the Reynolds-averaged Navier–Stokes equations" Open Physics, vol. 19, no. 1, 2021, pp. 853-862. Sun, Bohua. "Revisiting the Reynolds-averaged Navier–Stokes equations" Open Physics, vol. 19, no. 1, 2021, pp. 853-862.

Journal reference: Open Physics 2021, 19, 853-862
DOI: 10.1515/phys-2021-0102


The study found an error in current literature, including numerous textbooks, about the number of independent unknowns in the Reynolds stress tensor and/or in Reynolds-averaged Navier-Stokes equations (RANS). Current literature claims that the Reynolds stress tensor has six unknowns; however, this article shows that the Reynolds stress tensor only has independent three unknowns, which are functions of the three components of fluctuation velocity. This research discovers that the misconception about the number of independent unknowns in the RANS could stem from misinterpreting the Reynolds stress tensor. The misconception has hampered the development of turbulence for longtime. In order to find a way out of this difficult situation, we return to the time of Reynolds in 1895 and revisit Reynolds' averaging formulation of turbulence. The present investigation can be considered as a renaissance of Reynolds' work in 1895, which might shed light on the well-known closure problem of turbulence, and help to understand the puzzle of the turbulence closure problem that has eluded scientists and mathematicians for more than a century.


turbulence; number of unknowns; the Reynolds stress tensor; RANS; turbulence closure problem



Comments (1)

Comment 1
Received: 30 October 2019
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author
Comment: Removed one proof and two applications
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