  We carry out a principal component analysis of fluctuations in a hydrodynamic
simulation of heavy-ion collisions, and compare with experimental data from the
CMS collaboration. The leading and subleading principal components of elliptic
and triangular flow reproduce the trends seen in data. By contrast, the
principal components of multiplicity fluctuations show an interesting
difference in their $p_T$ dependence for simulations compared to experimental
data. Specifically, the leading component increases with $p_T$ in
hydrodynamics, while it is constant in experiment. In order to understand how
the leading and subleading modes arise, we construct a toy model where the
principal components have a simple analytic form. We show how the PCA
components depend on fluctuations of the average transverse momentum and of the
total multiplicity, as well as correlations between the two, and we verify that
hydrodynamic simulations agree with the predictions of the toy model. The
difference in the momentum trend is likely due to the fact that hydrodynamic
models typically have transverse momentum fluctuations that are larger than
seen experimentally.
