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تابع همبستگی
The subject of isotropic turbulence was in the air: on a visit to Caltech in 1936 and 1937, Leslie Howarth had collab- orated with von Ka愉ma慨 and developed the equation for two-point correlation functions in decaying isotropic turbulence (von Ka愉ma慨 and Howarth, 1938).
... it was hoped that some empirical connection might be discovered between these two kinds of functions, the results show that no single Eulerian two-point correlation function is a good approximation to the Lagrangian function, . . .
The results show that correlation functions for band-pass filtered veloci- ties decay at time-scales commensurate with the eddy-scale highlighted by the band-pass filtering.
erential equations for the two-point two-time velocity correlation function and the response function.
But Kraichnan noted that, when various correlation functions are expanded in terms of Feynman diagrams, the random coupling model retains only a sub- class of all diagrams; in particular it misses the so-called vertex corrections which contribute (in field-theoretic language) to the renormalization of the nonlinear interaction.9
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