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Already by the end of 1939, he had outlined the scheme of the mathematical description (of what we now call the Richardson cascade) based on self-similarity and predicted that E(p) for pl " 1 will be a power law but did not obtain the exponent (see Yaglom (1994) and Obukhov (1988, p. 83)).
Second and more important, it is still under the spell of two magic concepts of the Kol- mogorov school: Gaussianity and self-similarity.
Compared with KO41, the new version KO62 somehow pushes these two further down the road: the new (refined) self-similarity is local and Gaussianity is transfered to logarithms, re- placing additivity with multiplicativity.
As we now believe, direct turbulence cascades (from large to small scales) have, at a fundamental level, nothing to do with either Gaussianity or self-similarity, even though these concepts can help to design useful semi-empirical models for ap- plications.
An important paper in the development of the attached eddy hypothesis is Townsend (1961), which focused mainly on self-similar boundary layer flows and the structure in the log (equilibrium) region.
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