  Weak galaxy lensing surveys have consistently reported low values of the
$S_8$ parameter compared to the $\textit{Planck}\ \Lambda\rm{CDM}$ cosmology.
Amon & Efstathiou (2022) used KiDS-1000 cosmic shear measurements to propose
that this tension can be reconciled if the matter fluctuation spectrum is
suppressed more strongly on non-linear scales than assumed in state-of-the-art
hydrodynamical simulations. In this paper, we investigate cosmic shear data
from the Dark Energy Survey (DES) Year 3. The non-linear suppression of the
matter power spectrum required to resolve the $S_8$ tension between DES and the
$\textit{Planck}\ \Lambda\rm{CDM}$ model is not as strong as inferred using
KiDS data, but is still more extreme than predictions from recent numerical
simulations. An alternative possibility is that non-standard dark matter
contributes to the required suppression. We investigate the redshift and scale
dependence of the suppression of the matter power spectrum. If our proposed
explanation of the $S_8$ tension is correct, the required suppression must
extend into the mildly non-linear regime to wavenumbers $k\sim 0.2 h {\rm
Mpc}^{-1}$. In addition, all measures of $S_8$ using linear scales should agree
with the $\textit{Planck}\ \Lambda\rm{CDM}$ cosmology, an expectation that will
be testable to high precision in the near future.
