A family of dynamic subgrid-scale models consistent with asymptotic material frame indifference

It is claimed in the subgrid-scale (SGS) modeling of incompressible turbulent flows that none of the (modified) Leonard terms, the (modified) cross terms, or their sums can be neglected, in principle, due to the constraint of material frame indifference in the limit of two-dimensional turbulence [C. G. Speziale: Geophys. Astrophys. Fluid Dyn. 23 (1983) 69], and that the Clark model [R. A. Clark, J. H. Ferziger and W. C. Reynolds: J. Fluid Mech. 91 (1979) 1] is consistent with this constraint. Furthermore, a family of dynamic SGS models consistent with this constraint is found, and specifically, a two-parameter dynamic SGS model is proposed as the most desirable member, whose expression for the SGS Reynolds stress asymptotically disappears in the limit of two-dimensional turbulence.