Original Article 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 modelling

The present paper shows that the transport equations governing second order turbulent closures are form invariant, but remain frame dependent 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 Müller (1972) and today developed in the framework of the new concept of extended thermodynamics. Following this new concept, these relations are consequently incorporated as additional basic balance laws. The results are: 1) in the case of the Reynolds-stress-transport equation, this eliminates the so-called constraints imposed in [15–17, 19] on turbulence models; 2) to ensure the closure of the new set of basic balance laws, closure assumptions can then be considered as proper constitutive equations which must be restricted by the well known constitutive theory principles in extended thermodynamics. Received: April 4, 1996