Abstract
The functional formalism for turbulence mechanics originated with Hopf is generalized in such a way that it can embrace a space-time correlation tensor of turbulent fields, i.e. correlation tensor between non-simultaneous fields, and furthermore any external random forcing field can be taken into account in the formalism. The first work in this direction was recently done by Lewis and Kraichnan, but here the theory is more compactly and generally developed together with the deduction of a general solution of the full basic functional equations in terms of functional integration .
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