Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.
Only the linear viscous fluid is considered herein
along with the Reynolds decomposition. A uniqueness
theorem is presented for the mean motion equations
which shows that the Reynolds tensor is not uniquely
defined. The mean pressure field is also not unique.
Some implications of this non–uniqueness for the construction
of turbulence models are discussed. In particular,
the non–uniqueness allows a gauge field to be
introduced. One such field is Beltrami.