  Recent works on wall-bounded flows have corroborated the coexistence of
wall-attached eddies, whose statistical features are predicted through
Townsend's attached eddy hypothesis (AEH), and very-large-scale motions
(VLSMs), which are not encompassed in the AEH. Furthermore, it has been shown
that the presence of wall-attached eddies within the logarithmic layer is
linked to the appearance of an inverse-power-law region in the streamwise
velocity energy spectra, upon significant separation between outer and viscous
scales. In this work, a near-neutral atmospheric surface layer (ASL) is probed
with a wind LiDAR to investigate the contributions to the streamwise velocity
energy associated with wall-attached and VLSMs for a very-high Reynolds-number
boundary layer. Energy and linear coherence spectra (LCS) of the streamwise
velocity are interrogated to identify the spectral boundaries associated with
eddies of different typologies and the maximum height attained by wall-attached
eddies. Inspired by the AEH, an analytical model for the LCS associated with
wall-attached eddies is formulated. The experimental results show that the
identification of the wall-attached-eddy energy contribution through the
analysis of the energy spectra leads to an underestimate of the associated
spectral range, maximum height attained, and turbulence intensity. This feature
is due to the overlap of the energy associated with VLSMs obscuring the
inverse-power-law region. On the other hand, the Townsend-Perry constant for
the turbulence intensity seems to be properly estimated through the spectral
analysis. The LCS analysis estimates wall-attached eddies with a
streamwise/wall-normal ratio of about 14.3 attaining a height of about 30% of
the outer scale of turbulence.
