On turbulent Reynolds stress closure and modern continuum mechanics

The problem of Reynolds stress closure in turbulence is examined with reference to its consistency with the basic principles of modern continuum mechanics. It is proven that Reynolds stress closure is completely consistent with the principles of determinism and material frame-indifference. The situation is particularly clear as regards frame-indifference. Since the Reynolds stresses are defined kinematically, their transformation properties under a change of frame can be mathematically determined. The consequences that this has on turbulence modeling are discussed.