Abstract
We study the experimental dependence of the third-order velocity structure function on the Taylor based Reynolds number, obtained in different flow types over the range 72⩽Rλ⩽2260. As expected, when the Reynolds number is increasing, the third-order velocity structure functions (plotted in a compensated way) converge very slowly to a possible −4/5 plateau value according to the Kolmogorov 41 theory. Actually, each of these normalized third-order functions exhibits a maximum, at a scale close to the Taylor microscale λ. In this Brief Communication, we show that experimental data are in good agreement with the recent predictions of Qian and Lundgren. We also suggest that, from an experimental point of view, a log-similar plot suits very well to study carefully the behavior of the third-order velocity structure functions with the flow Reynolds number.
Highlights
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Even though the previous relation is strictly valid for Reynolds number tending to the infinity, experimental data seemed to verify it as soon as a conspicuous power-law scaling range existsi.e., for Rу500), whatever the flow type
Summary
Yves Gagne Institut de Mecanique de Grenoble, LEGI, UJF/INPG/CNRS, BP 53, 38041-Grenoble-Cedex 9, France. Even though the previous relation is strictly valid for Reynolds number tending to the infinity, experimental data seemed to verify it as soon as a conspicuous power-law scaling range existsi.e., for Rу500), whatever the flow type. It is difficult to decide if an experimental discrepancy with the Lundgren prediction is due toia peculiar injection regime as discussed by Qian, ͑iian intermittency effect, ͑iiior, an experimental error in the determination of R. At the particular scale where S3(r) is maximum, the above relation leads to From this Reynolds dependence ofS3(r)͔max , Qian has deduced several predictions of the exponent depending on the types of flow. For some types of large-scale forcing turbulence, he predicted an exponent equal to ϭ6/5, in agreement with the Moisy experiments.
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