Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On the Reynolds-Averaged Navier-Stokes Equations

Version 1 : Received: 30 June 2019 / Approved: 2 July 2019 / Online: 2 July 2019 (09:53:19 CEST)

How to cite: Sun, B. On the Reynolds-Averaged Navier-Stokes Equations. Preprints 2019, 2019070038 (doi: 10.20944/preprints201907.0038.v1). Sun, B. On the Reynolds-Averaged Navier-Stokes Equations. Preprints 2019, 2019070038 (doi: 10.20944/preprints201907.0038.v1).


This paper attempts to clarify an long-standing issue about the number of unknowns in the Reynolds-Averaged Navier-Stokes equations (RANS). This study shows that all perspectives regarding the numbers of unknowns in the RANS stem from the misinterpretation of the Reynolds stress tensor. The current literature consider that the Reynolds stress tensor has six unknown components; however, this study shows that the Reynolds stress tensor actually has only three unknown components, namely the three components of fluctuation velocity. This understanding might shed a light to understand the well-known closure problem of turbulence.


turbulence; the Reynolds stress tensor; turbulence closure problem



Comments (1)

Comment 1
Received: 2 July 2019
The commenter has declared there is no conflict of interests.
Comment: This paper presents an interesting and important topics about the number of degrees of freedom in the Reynolds stress. In all text books, it is stated that there are 6 degrees of freedom for the second-order symmetric Reynolds stress tensor. However, based on the velocity decomposition, the author proposed 3 unknowns in the Reynolds stress. If the NS equations can really describe the turbulence, the turbulence theoretically could be described in a deterministic way, and the velocity decomposition in this paper seems reasonable. I am very happy to see the idea in this paper. There may have BIG mistake in the traditional modeling of the Reynolds stress. Thank the author to give us a chance to re-think of this fundamental problem. Turbulence modeling may possibly be reconstructed according to the idea in this paper.
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