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

It is claimed in the subgrid-scale (SGS) modeling of incompressible turbule nt flows that none of the (modified) Leonard terms, the (modified) cross te rms, 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 Cl ark model [R. A. Clark, J. H. Ferziger and W. C. Reynolds: J. Fluid Mech. 9 1 (1979) 1] is consistent with this constraint. Furthermore, a family of dy namic SGS models consistent with this constraint is found, and specifically , a two-parameter dynamic SGS model is proposed as the most desirable membe r, whose expression for the SGS Reynolds stress asymptotically disappears i n the limit of two-dimensional turbulence.