| Abstrakt: |
Measurement data sets are presented for the turbulence intensity profile of three velocity components ($u$ , $v$ and $w$) and turbulent kinetic energy (TKE, $k$) over a wide range of Reynolds numbers from $Re_\tau =990$ to 20 750 in a pipe flow. The turbulence intensity profiles of the $u$ - and $w$ -component show logarithmic behaviour, and that of the $v$ -component shows a constant region at high Reynolds numbers, $Re_\tau >10\,000$. Furthermore, a logarithmic region is also observed in the TKE profile at $y/R=0.055\unicode{x2013}0.25$. The Reynolds number dependences of peak values of $u$ -, $w$ -component and TKE fit to both a logarithmic law (Marusic et al. , Phys. Rev. Fluids , vol. 2, 2017, 100502) and an asymptotic law (Chen and Sreenivasan, J. Fluid Mech. , vol. 908, 2020, R3), within the uncertainty of measurement. The Reynolds number dependence of the bulk TKE $k^+_{bulk}$ , which is the total amount of TKE in the cross-sectional area of the pipe also fits to both laws. When the asymptotic law is applied to the $k^+_{bulk}$ , it asymptotically increases to the finite value $k^+_{bulk}=11$ as the Reynolds number increases. The contribution ratio $\langle u'^2\rangle /k$ reaches a plateau, and the value tends to be constant within $100 at $Re_\tau >10\ 000$. Therefore, the local balance of each velocity component also indicates asymptotic behaviour. The contribution ratios are balanced in this region at high Reynolds numbers as $\langle u'^2\rangle /k\simeq 1.25$ , $\langle w'^2\rangle /k\simeq 0.5$ and $\langle v'^2\rangle /k \simeq 0.25$. [ABSTRACT FROM AUTHOR] |
