Decay Power Law in, High Intensity, Isotropic Turbulent Flow*

In the study reported here, isotropy is determined using the measure proposed by George (1992), where isotropy corresponds to those downstream positions where the product of the Taylor Reynolds number and the skewness of the velocity derivative is a constant. Straight forward approach can be used which is based on the observation of Batchelor (1953), that the square of the Talor micorscale is linearly related to downstream distance relative to the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for mean velocities of 6 and 8 m/s for the downstream decay of the parameters listed in the preceding. The corresponding values of the Taylor Reynolds number at the start of the isotropic region are 290 and 400, and the variance decay exponent and virtual origin are found to be respectively -1.707 and -1.298 and -27.95 and -5.757. The exponents in the decay law for the other parameters are found to be within $\pm$ 3\% of the expected values.