Preprint Article Version 1 This version is not peer-reviewed

Closed integral-differential equations of incompressible Navier-Stokes turbulent flow

Version 1 : Received: 31 July 2018 / Approved: 31 July 2018 / Online: 31 July 2018 (12:37:13 CEST)
Version 2 : Received: 22 September 2018 / Approved: 24 September 2018 / Online: 24 September 2018 (13:03:40 CEST)

How to cite: Sun, B. Closed integral-differential equations of incompressible Navier-Stokes turbulent flow. Preprints 2018, 2018070622 (doi: 10.20944/preprints201807.0622.v1). Sun, B. Closed integral-differential equations of incompressible Navier-Stokes turbulent flow. Preprints 2018, 2018070622 (doi: 10.20944/preprints201807.0622.v1).

Abstract

This paper showed that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literature has stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We showed the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. With this understanding, the closed Reynolds Navier-Stokes turbulence equations of incompressible flows were formulated. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

Subject Areas

Turbulence, the Reynolds stress tensor, turbulence closure problem

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