  This paper deals with determination of turbulent convection velocities from
particle image velocimetry (PIV). Turbulent convection velocities are of
interest because they can be used to map temporal information into space.
Convection velocity can be defined in several different ways. One approach is
to use the phase-spectrum of two signals with a time-separation. Obtaining
convection velocity per wavenumber involves determining a spatial spectrum. PIV
data is limited in spatial resolution and sample length. The influence of
truncation of both spatial resolution and frequency resolution is investigated,
as well as the influences of spatial filtering and measurement noise. These
issues are investigated by using a synthetic data set obtained by creating
velocity-time data with an imposed spectrum. Results from the validation show
that, when applying a Hamming window before determining the phase spectrum,
there is a usable range of wavenumbers for which convection velocities can be
determined. Simulation of flow evolution, movement into and out of the
measurement plane, and measurement noise show that these result in a spread in
convection velocities using the current approach. Despite this spread, the most
probable calculated convection velocity coincides with the imposed convection
velocity. Application of the phase-spectral approach to a turbulent boundary
layer with $Re_\tau \approx 2700$, shows there is a range of convection
velocities and that the most probable convection velocity is equal to the local
mean velocity.
