  Wall turbulence is a ubiquitous phenomenon in nature and engineering
application, yet predicting such turbulence is difficult due to its complexity.
High-Reynolds-number turbulence, which includes most practical flows, is
particularly complicated because of its wide range of scales. Although the
attached-eddy hypothesis postulated by Townsend can be used to predict
turbulence intensities and serves as a unified theory for the asymptotic
behaviors of turbulence, the presence of attached structures has not been
confirmed.Here, we demonstrate the logarithmic region of turbulence intensity
by identifying wall-attached structures of velocity fluctuations ($u_i$)
through direct numerical simulation of a moderate-Reynolds-number boundary
layer ($Re_\tau \approx 1000$). The wall-attached structures are self-similar
with respect to their heights ($l_y$), and in particular the population density
of the streamwise component ($u$) scales inversely with $l_y$, which is
reminiscent of the hierarchy of attached eddies. The turbulent intensities
contained within the wall-parallel components ($u$ and $w$) exhibit the
logarithmic behavior. The tall attached structures ($l_y^+ > 100$) of $u$ are
composed of multiple uniform momentum zones (UMZs) with a long streamwise
extent, whereas those of the cross-stream components ($v$ and $w$) are
relatively short with a comparable width, suggesting the presence of tall
vortical structures associated with multiple UMZs. The magnitudes of the
near-wall peak observed in the streamwise turbulent intensity increase with
increasing $l_y$, reflecting nested hierarchies of the attached $u$ structures.
These findings suggest that the identified structures are prime candidates for
Townsend's attached-eddy hypothesis and serve as cornerstones for understanding
the multiscale phenomena of high-Reynolds-number boundary layers.
