Variation of the slope of the velocity power spectrum and intermittency factor corresponding to 160 \textless\ Re$_{\lambda}$ \textless\ 490

ORAL

Abstract

It has been observed in many studies, at sufficiently high Reynolds number and for an intermediate range of wavelengths that $E_{11} (\kappa )\sim \kappa^{-n}$. Kolmogorov's 1$^{\mathrm{st}}$ and 2$^{\mathrm{nd}}$ hypotheses state that $n$ should approach 5/3 as the Reynolds number tends to infinity and that the variation of $n$ from 5/3 is due to intermittency in the dissipation. Wind tunnel experiments are conducted where high intensity turbulence is generated by means of an active turbulence grid modeled after Makita's 1991 design (Makita, 1991) as implemented by Mydlarski and Warhaft (M{\&}W, 1998). The goal of this study is to document the variation of $n$ over a range of Re$_{\lambda}$ from 160 to 490. The corresponding values of $n$ are 1.46 and 1.55 where $n=5/3-3.23Re_{\lambda }^{-0.56} $. This is in disagreement with Mydlarski and Warhaft who found that $n=5/3-5.25Re_{\lambda }^{-2/3} $. The intermittency factor, $\mu $, is obtained from the slope of the dissipation spectrum where $E_{11}^{\varepsilon } (\kappa )\sim \kappa^{\mu -1}$ and its variation is determined. The intermittency factor is calculated using the spatial derivative of the downstream velocity as determined from the temporal derivative and Taylor's hypothesis. As turbulence intensity increases, it had been hypothesized that $\mu $ would become zero. However, Sreenivasan and Kailasnath (S{\&}K, 1992), in agreement with Praskovsky and Oncley (P{\&}O, 1994), have found that $\mu $ appears to be nearly a constant of $0.25\pm 0.05$. In the current study it is found that the intermittency exponent is nearly a constant, in agreement with Sreenivasan and Kailasnath, but has a value of 0.7.

Authors

  • Alejandro Puga

    University of California, Irvine