In wall turbulence, meandering behaviors of large-scale structures observed in the logarithmic layer are a crucial spatial feature to understand the spatial organization of these structures and to improve the structure-based turbulence model. These structures extend from the near-wall region to the edge of boundary layers $\left(\delta \right)$. Thus, their meandering motions leave an imprint on the two-point turbulence statistics across the flow, especially in the logarithmic region. Herein, we demonstrate the influence of the meandering motions of wall-attached structures on the two-point correlation and the premultiplied two-dimensional spectra by analyzing the direct numerical simulation data of the turbulent boundary layer at ${\text{Re}}_{\tau }\approx 1000$. The meandering magnitudes of wall-attached structures increase with their height $\left(l_y\right)$ but significantly differ among the identified structures even at a given $l_y$. In addition, the wall-attached structures of streamwise velocity fluctuations $\left(u\right)$ are found to be aligned along with a preferred spanwise offset regardless of the meandering motion. This feature is confirmed through the conditional two-point correlations of $u$ within the meandering structures, which leads to a distinct X pattern in the logarithmic region. We further examine the spectral behavior of the meandering structures across the streamwise and spanwise wavelengths (${\lambda }_x$ and ${\lambda }_z$, respectively) through the premultiplied two-dimensional spectra. With increasing meandering magnitudes, the energy spectra are more inclined to the ${\lambda }_z$ direction. Furthermore, the energy spectra of the strong meandering structures are bounded by a linear relationship ${\lambda }_x\sim {\lambda }_z$ over the large-scale range, reminiscent of self-similar scaling predicted by the attached-eddy hypothesis. In particular, the upper bound is aligned along ${\lambda }_x\approx 2{\lambda }_z$ over ${\lambda }_z>\delta$, which is absent in the energy spectral of the total $u$. This result reveals that the meandering motions allow the large-scale structures to contain wide spanwise scale energy that is self-similar in the logarithmic region. Finally, a discussion on the near-wall parts of the meandering structures is given with an emphasis on Townsend's inactive eddies.

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• Boundary layers
• Turbulence