Contribution of attached eddies to the intensity and turbulent transfer of velocity fluctuations in wall-turbulence

Abstract

We validated a model that was recently derived by Mouri (2017) for the twopoint correlation function of the streamwise velocity fluctuation u in wallturbulence by using experimental boundary layer data. The model expresses the correlation function as the superposition of the contributions from the main eddies located at the height where the correlation is evaluated and the attached eddies located above. These contributions were quantified as a function of r/y, where r is the streamwise distance and y is the height from the wall, and evaluated by using the data. The contribution from the main eddies exhibits logarithmic dependence for r/y=O(1), and that from the attached eddies occurs only for r/y=O (10), where it also decays logarithmically with r/y. Furthermore, the model was extended to include the wall-normal energy flux due to turbulent convection, by assuming that the flux consists of the selfsimilar transfer of main eddies, and the transfer of the larger attached eddies. It was found that the flux of u 2 was expressed well by the extended model, and the two contributions were evaluated using the experimental data. Both types of eddies are strongly convected upward and downward; however, for the attached eddies, most of the fluxes in the opposite directions cancel out, leading to a reduced contribution to the net flux.

Logarithmic and nonlogarithmic scaling laws of two-point statistics in wall turbulence

“…3, data points of u(x, z)u(x+r, z) c make up linear functions of ln(δ 99 /z). The same has been observed in a laser Doppler anemometry of a similar flow [17]. By fitting Eq.…”

“…The ratio r/δ has accordingly been used as a parameter of two-point statistics [34,35]. However, in our results and in some others [17,19], those structures are not discernible. They are meandering so that their total lengths do not appear in one-dimensional correlations and spectra.…”

“…(3a) has been derived without adding any assumption to the original hypothesis of Townsend [5]. Although previous studies added assumptions [15][16][17][18], they are not consistent with that hypothesis if their results do not satisfy Eq. (3a), aside from whether they appear reasonable or not [11,19].…”