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It is worth pointing out that Eq. (28) involves a line average of the structure-function parameter, whereas Kolmogorov's (Ref. 12) theory of interminent turbulence explicitly deals only with volume averages. This issue did not arise in a previous paper I coauthored (Ref. 16), since the scattering treatment in that paper involved volume averages of structure functions. Fortunately there is good reason to think that Kolmogorov's log-normal model also applies to line averages. The derivation presented by Gurvich and Yaglom (Ref. 20) in favor of the log-normal law applies to line averages just as well as volume averages. In fact, experimental verification of the log-normal model has generally relied on line averages.
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In Ref. 2, primes were used to indicate the propagation coordinates. The unprimed coordinate system was the meteorological coordinates. I have used the opposite convention in this paper, in order to be consistent with the presentation of the isotropic models.
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