Spatial Variation of Statistical and Spectral Properties of the Stream Wise and Wall-Normal Velocity Fluctuations in the Near-Neutral Atmospheric Surface Layer

Abstract

Based on high-quality near-neutral atmospheric-surface-layer (ASL) data obtained from an observational site located in flat desert and existing experimental results for a friction Reynolds number Re_τ < 10⁶, the spatial variation of the streamwise and wall-normal velocity statistics and the Re_τ dependence of the scaling parameters are investigated. The near-neutral ASL results show that, for Re_τ > 10⁶, the change of the second-order statistics of the streamwise velocity component with height is consistent with the experimental results for Re_τ < 10⁶, while the second-order statistics of the wall-normal velocity component increase linearly with height. In combination with the experimental results for Re_τ < 10⁶, the variation of the slope of streamwise turbulence intensity with height and the variation of the slope and intercept of the wall-normal turbulence intensity with height are quantified to reveal that both the streamwise and wall-normal velocity variances follow a generalized logarithmic law, with the distribution of the streamwise and wall-normal velocity components satisfying sub- and super-Gaussian distributions. Spectral analysis shows that the variation of the wavenumber corresponding to the pre-multiplied streamwise and wall-normal spectra peaks with the ratio z/δ obeys the form $k_{x} \delta = a(\delta /z)^{b}$, where z is the height, k_x is the streamwise wavenumber, and δ is the ASL thickness. For the pre-multiplied streamwise spectra, $b = 0.5 \pm 0.1$ and the value of a may have a Reynolds-number dependence, while for the pre-multiplied wall-normal spectra, $a = 2.2 \pm 0.09$ and $b = 1.0 \pm 0.1$. The von Kármán constant, the Townsend–Perry constant and other parameters also display a weak Reynolds-number dependence.