Comparison between the sum of second-order velocity structure functions and the second-order temperature structure function

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Abstract
The previously established similarity between the temperature spectrum and the spectrum corresponding to the mean turbulent energy in a wide variety of turbulent (shear) flows is re‐examined within the framework of second‐order velocity and temperature structure functions. Measurements in a turbulent wake indicate that Dq, the sum of the three second‐order velocity structure functions bears close similarity to Dθ, the second‐order temperature structure function, when Dq and Dθ are normalized by the mean turbulent energy and temperature variance, respectively. This similarity also applies to other flows. In the limit of small separations, the Kolmogorov‐normalized structure functions differ only by the value of the molecular Prandtl number. In the inertial range, the Obukhov–Corrsin constant differs from the Dq Kolmogorov constant by a factor equal to the dissipation time scale ratio. This ratio is typically about 0.5.