Approximation accuracy of the two-point third moments of the velocity field in the homogeneous turbulence

Different approximations for two-point third moments of velocity field appearing in the Karman–Howart equation are compared. For this purpose, the known experimental results of Townsend and Stewart and the model form of turbulence energy spectrum, which enables approximating the experimentally determined second moments of velocity field, are used. The latter are applied for evaluation of the two-point third moments by the procedures proposed by various authors. Calculation results are compared to experimental data, which allows obtaining quantitative assessments of approximation accuracy. For a number of models, the second-order structural function is found from the Kolmogorov equation for inertial subrange. Thus, in the Hasselman and Lytkin models for the structural function DLL the power law expected in the inertial subrange DLL(r) ∼ r2/3 is obtained.