Abstract

Properties of the Reynolds stress fluctuations in the inertial sublayer of canonical turbulent boundary layer, channel and pipe flows are explored. A broader aim here is to investigate if the self-similar properties associated with the mean momentum balance (MMB) in these flows are also reflected in the statistics of the turbulent motions responsible for wall-normal momentum transport. Toward this aim, a succinct summary of analytical properties admitted by the MMBs associated with these flows is used to motivate the study of the $ uv $ fluctuations, where $u$ and $v$ are the streamwise and wall-normal velocity fluctuations, respectively. Statistical properties of primary interest are associated with the time fraction that $ uv $ time series are negative (or equivalently the negative area fraction in a wall-parallel planes), $T_{24}$, the skewness of $uv$, S($uv$), and the $uv$ correlation coefficient, $r$—all of which are properties associated with the underlying $uv$ probability distribution (pdf). These and other properties of the Reynolds stress fluctuations are examined in the inertial sublayer of fully developed channel and pipe flows and zero pressure gradient turbulent boundary layers. The data sources include channel flow direct numerical simulations up to friction Reynolds numbers, $\delta ^{= 8,000$, laboratory pipe and boundary layer experiments (up to $\delta} exceeding 10,000$), and field measurements in the near-neutral atmospheric surface layer, where $\delta ^{= O(1 \times 10}6)$. The analyses indicate that, to within the accuracy of the measurements, both $T_{24}$ and S($uv$) approach values that correlate with the similarity stretching parameter revealed in the MMB analysis, the $uv$ pdf exhibits self-similarity over the entire $\delta^{$ range, a Gram-Charlier expansion based analysis of the $uv$ pdf shows that the assumption of Gaussian $u$ and $v$ statistics provides a good approximation for $T_{24}$, and that $r$ (which is a key parameter in the Gram-Charlier representation) exhibits an approximately $-1/4$ power-law decay with $\delta}+$.