Naively, velocity fields of order (see e.g. [Strauss & Willick, 1995] for a review) and
optical depths of a few percent would imply a Doppler effect that rivals the
acoustic peaks themselves. That this is not the case is the joint consequence
of the cancellation described in §4.2.1
and the fact that the acoustic peaks are not ``Doppler peaks'' (see §3.8).
Since the Doppler effect comes from the peculiar velocity along the line of
sight, it retains no contributions from linear modes with wavevectors perpendicular
to the line of sight. But as we have seen, these are the only modes that survive
cancellation (see Plate 3 and [Kaiser, 1984]). Consequently, the Doppler effect
from reionization is strongly suppressed and is entirely negligible below
unless the optical depth in the reionization epoch approaches
unity (see Plate 5b).