  For wall-bounded turbulent flows, Townsend's attached eddy hypothesis
proposes that the logarithmic layer is populated by a set of energetic and
geometrically self-similar eddies. These eddies scale with a single length
scale, their distance to the wall, while their velocity scale remains constant
across their size range. To investigate the existence of such structures in
fully developed turbulent pipe flow, stereoscopic particle image velocimetry
measurements were performed in two parallel cross-sectional planes, spaced
apart by a varying distance from 0 to 9.97$R$, for $Re_\tau = 1310$, 2430 and
3810.
  The instantaneous turbulence structures are sorted by width using an
azimuthal Fourier decomposition, allowing us to create a set of average eddy
velocity profiles by performing an azimuthal alignment process. The resulting
eddy profiles exhibit geometric self-similar behavior in the $(r,\theta)$-plane
for eddies with spanwise length scales ($\lambda_\theta/R$) spanning from 1.03
to 0.175. The streamwise similarity is further investigated using two-point
correlations between the two planes, where the structures exhibit a
self-similar behaviour with length scales ($\lambda_\theta/R$) ranging from
approximately $0.88$ to $0.203$. The candidate structures thereby establish
full three-dimensional geometrically self-similarity for structures with a
volumetric ratio of $1:80$. Beside the geometric similarity, the velocity
magnitude also exhibit self-similarity within these ranges. However, the
velocity scale depends on eddy size, and follow the trends based on the scaling
arguments proposed by \cite{Perry1986}.
