  Self-similarity of wall-attached coherent structures in a turbulent channel
at $Re_\tau=543$ is explored by means of resolvent analysis. In this modelling
framework, coherent structures are understood to arise as a response of the
linearised mean-flow operator to generalised, frequency-dependent Reynolds
stresses, considered to act as an endogenous forcing. We assess the
self-similarity of both the wall-attached flow structures and the associated
forcing. The former are educed from direct numerical simulation data by finding
the flow field correlated with the wall shear, whereas the latter is identified
using a frequency space version of Extended Proper Orthogonal Decomposition
(Bor\'{e}e, J. 2003 Extended proper orthogonal decomposition: a tool to analyse
correlated events in turbulent flows. Experiments in fluids 35 (2), 188-192).
The forcing structures identified are compared to those obtained using the
resolvent-based estimation introduced by Towne \emph{et al}. (Towne, A.,
Lozano-Dur\'{a}n, A. & Yang, X. 2020 Resolvent-based estimation of space-time
flow statistics. Journal of Fluid Mechanics 883, A17). The analysis reveals
self-similarity of both wall-attached structures$-$in quantitative agreement
with Townsend's hypothesis of self-similar attached eddies$-$and the underlying
forcing, at least in certain components.
