  X-ray diffraction measurements show that the high-temperature superconductor
YBa$_2$Cu$_3$O$_{6.54}$, with ortho-II oxygen order, has charge density wave
order (CDW) in the absence of an applied magnetic field. The dominant
wavevector of the CDW is $\mathbf{q}_{\mathrm{CDW}} = (0, 0.328(2), 0.5)$, with
the in-plane component parallel to the $\mathbf{b}$-axis (chain direction). It
has a similar incommensurability to that observed in ortho-VIII and ortho-III
samples, which have different dopings and oxygen orderings. Our results for
ortho-II contrast with recent high-field NMR measurements, which suggest a
commensurate wavevector along the $\mathbf{a}$-axis.
  We discuss the relationship between spin and charge correlations in
YBa$_2$Cu$_3$O$_{y}$, and recent high-field quantum oscillation, NMR and
ultrasound experiments.
