Abstract
Proofs are given which show that the integral representations for the Navier‐Stokes spatial correlation functions satisfy the reality conditions, the continuity conditions, and the Navier‐Stokes condition. With the aid of the integral representations for the correlation functions an analysis of the decay of homogeneous turbulence is developed. For the initial period of decay the theory predicts the empirical law u2 α ν(t″ − t′)−1, as well as a universal and shape‐preserving two‐point correlation tensor.
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