Why is the Reynolds Stress Realizable, but Not Objective?

The Coriollis Theorem of classical kinematics predicts that the strain rate is temporally frame insensitive for all turbulent flows; and, that the Reynolds stress is temporally frame sensitive for all turbulent flows. Consequently, the Cauchy stress and the Reynolds stress are not similar. Most significantly, the Reynolds stress predicts that the turbulent dispersion and the turbulent dissipation of turbulent kinetic energy are both positive; and, the production of kinetic energy could be either positive or negative. See Koppula K.S., A. Benard, and C. A. Petty, 2009, Realizable Algebraic Reynolds Stress Closure, Chem. Eng. Sci., 64, 4611.