ON THE FRAME DEPENDENCE AND FORM INVARIANCE OF THE TRANSPORT-EQUATIONS FOR THE REYNOLDS STRESS TENSOR AND THE TURBULENT HEAT-FLUX VECTOR - ITS CONSEQUENCES ON CLOSURE MODELS IN TURBULENCE MODELING

The present paper shows that the transport equations governing second order turbulent closures are form invariant, but remain frame dependen t through the emergence of the body force; thus they do not fulfil the principle of material frame indifference as formulated by Truesdell & Noll (1965). However, this frame dependence corresponds to that first discussed by Muller (1972) and today developed in the framework of th e new concept of extended thermodynamics. Following this new concept, these relations are consequently incorporated as additional basic bala nce laws. The results are: 1) in the case of the Reynolds-stress-trans port equation, this eliminates the so-called constraints imposed in [1 5-17, 19] on turbulence models; 2) to ensure the closure of the new se t of basic balance laws, closure assumptions can then be considered as proper constitutive equations which must be restricted by the well kn own constitutive theory principles in extended thermodynamics.