On the Reynolds-Averaged Navier-Stokes Equations

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.