When developing turbulence modelling from scratch certain questions arise which inevitably turn into methodological problems regarding this topic
What makes Euclidean transformations in classical continuum mechanics, in particular turbulence modelling, so special ?
Why is frame-dependency in all unclosed terms of existing algebraic models, e.g. in the Reynolds-stress tensor, always only modelled by the mean objective intrinsic spin tensor, i.e. the mean vorticity tensor measured in a rotating frame relative to an inertial frame: 〈
〉 = 〈
Why is the mean pressure or one of its gradients never taken along as a closure variable ?
Why does there still not exist a clear-cut mathematical formulation of the material frame-indifference (MFI)-principle in general continuum mechanics (if it applies as a physical approximation for reducing constitutive equations) ? What consequences does a proper mathematical formulation have for modelling turbulence in the limit of a 2D flow state ?
Answers to these questions are given herein, except for the last question which is beyond the scope of this article . From the outset it is clear, that in order to give an unambiguous answer to these interlinked questions one needs a new mathematical framework, or more precisely, a setting of universal form-invariance (UFI) which extends the classical framework of an Euclidean geometry being used so far .