Measures of Anisotropy and the Universal Properties of Turbulence
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Local isotropy, or the statistical isotropy of small scales, is one of the basic assumptions underlying Kolmogorov's theory of universality of small-scale turbulent motion. While, until the mid-seventies or so, local isotropy was accepted as a plausible approximation at high enough Reynolds numbers, various empirical observations that have accumulated since then suggest that local isotropy may not obtain at any Reynolds number. These notes examine in some detail the isotropic and anisotropic contributions to structure functions by considering their SO(3) decomposition. Viewed in terms of the relative importance of the isotropic part to the anisotropic parts of structure functions, the basic conclusion is that the isotropic part dominates the small scales at least up to order 6. This follows from the fact that, at least up to that order, there exists a hierarchy of increasingly larger power-law exponents, corresponding to increasingly higher-order anisotropic sectors of the SO(3) decomposition. The numerical values of the exponents deduced from experiment suggest that the anisotropic parts in each order roll off less sharply than previously thought by dimensional considerations, but they do so nevertheless.
REsubmitting abstract to fit required length. Submitted in one .tar.gz file containing Tex source + figures + .bbl file. These are lecture/review notes and so rather large. 23 EPS figures (one of them --j1_table.eps -- is inserted in a table environment)
REsubmitting abstract to fit required length. Submitted in one .tar.gz file containing Tex source + figures + .bbl file. These are lecture/review notes and so rather large. 23 EPS figures (one of them --j1_table.eps -- is inserted in a table environment)