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Kubo type time correlation formulae for turbulent transport coefficients in incompressible but heat conducting fluids are derived, especially for eddy viscosity, eddy heat conductivity, and pressure. The connection to the cascade method as well as its equivalence to the methods of closure of hierarchy are established. Lagrangean time integration is used. If the retarded Green’s function has exponential time behaviour the damping constant Γ q  can be calculated explicitely. In this approximation in the inertial range one finds the Kolmogoroff k -5/3  spectrum including its numerical factor (C=1.53). This induces a frequency spectrum ∼ ω  -2 .

Turbulent Transport Equations and Kubo Formulae for Eddy Transport Coefficients