REMARKS ON TURBULENT CONSTITUTIVE RELATIONS

The paper demonstrates that the concept of turbulent constitutive relations introduced by Lumley [1] can be used to construct general models for various turbulent correlations. Some of Generalized Cayley-Hamilton formulas for relating tensor products of higher Extension to tensor products of lower Extension are introduced. The combination of dimensional analysis and invariant theory can lead to ''turbulent constitutive relations'' (or general turbulence models) for, in principle, any turbulent correlations. As examples, the constitutive relations for Reynolds stresses and scalar fluxes are derived. The results are consistent with ones from RNG theory and two-scale DIA method, but with a more general form.