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Applicability of Kolmogorov’s and Monin’s equations of turbulence. (English) Zbl 0903.76044
Results are obtained for the second- and third-order statistics on the basis of local homogeneity without use of local isotropy. Accuracy of Kolmogorov’s equation is shown to be more sensitive to anisotropy of the third-order structure function than to anisotropy of the second-order structure function. Kolmogorov’s 4/5 law for the inertial range of the third-order structure function is obtained without use of the incompressibility conditions on the second- and third-order structure functions. A generalization of Kolmogorov’s 4/5 law, which applies to the inertial range of locally homogeneous turbulence at very large Reynolds numbers, is shown to also apply to the energy-containing range for the more restrictive case of stationary, homogeneous turbulence. The variety of derivations of Kolmogorov’s and Monin’s equation leads to a wide range of applicability to experimental conditions, including, in some cases, turbulence of moderate Reynolds number.

MSC:
76F99 Turbulence
76F05 Isotropic turbulence; homogeneous turbulence
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