Data-driven spectral filters for decomposing the streamwise turbulent kinetic energy in turbulent boundary layers

An organization in wall-bounded turbulence is evidenced by the classification of distinctly different flow structures, including large-scale motions such as hairpin packets and very large-scale motions or superstructures. In conjunction with less organized turbulence, these flow structures all contribute to the streamwise turbulent kinetic energy $\langle u^2\rangle$. Since different class structures comprise dissimilar scalings of their overlapping imprints in the streamwise velocity spectra, their coexistence complicates the interpretation of the wall-normal trend in $\langle u^2\rangle$ and its Reynolds number dependence. Via coherence analyses of two-point data in boundary layers we derive spectral filters for stochastically decomposing the streamwise spectra into sub-components, representing different types of statistical flow structures. It is also explored how the decomposition reflects the spectral break-down following the modeling attempts of Perry \emph{et al.} 1986 and Marusic \& Perry 1995. In the process we reveal a universal wall-scaling for a portion of the outer-region turbulence that is coherent with the near-wall region for $Re_{\tau} \sim O(10^3)$ to $O(10^6)$, which is described as a wall-attached self-similar structure embedded within the logarithmic region.