Modelling of subgrid-scale fluxes

Both necessary and sufficient conditions are derived in a systematic, rigorous way for a subgrid-scale (SGS) flux vector model to preserve the frame-indifference of the vector and to satisfy both the principle of material frame-indifference (PMFI) and the second law of thermodynamics. This leads to the results either confirming the previous intuitive arguments or offering new insights into turbulence modeling, and is of significance in clarifying some controversies in the literature, examining how well existing models preserve the physics, and developing new models.