REMARKS ON TURBULENT CONSTITUTIVE RELATIONS

The paper demonstrates that the concept of turbulent constitutive rela tions introduced by Lumley [1] can be used to construct general models for various turbulent correlations. Some of Generalized Cayley-Hamilt on formulas for relating tensor products of higher Extension to tensor products of lower Extension are introduced. The combination of dimens ional analysis and invariant theory can lead to ''turbulent constituti ve relations'' (or general turbulence models) for, in principle, any t urbulent correlations. As examples, the constitutive relations for Rey nolds stresses and scalar fluxes are derived. The results are consiste nt with ones from RNG theory and two-scale DIA method, but with a more general form.