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

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 D_q, the sum of the three second-order velocity structure functions bears close similarity to D_θ, the second-order temperature structure function, when D_q and D_θ, 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 D_q Kolmogorov constant by a factor equal to the dissipation time scale ratio. This ratio is typically about 0.5.