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Application of Central Limit Theorems to Turbulence Problems,
PENNSYLVANIA STATE UNIV UNIVERSITY PARK
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It is shown that to the extent that the moments involved exist the existence not 0 of all generalized integral scales is necessary and sufficient if all moments exist for integrals over adjacent segments of a stationary process to become asymptotically independent, and sufficient to ensure that existing moments of integrals will become Gaussian. The conditions under which several recent central limit and related theorems for dependent variables have been proven, are shown to be closely related to this requirement. As a consequence of this examination, a slight weakening is suggested of the common condition that the spectrum be non-zero. It is shown that dispersion in homogeneous turbulence is unlikely to be explicable on the basis of a central limit theorem. Author
APPROVED FOR PUBLIC RELEASE