A uniqueness theorem in fluid turbulence

Abstract

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.