  It has been argued recently that the galaxy peculiar velocity field provides
evidence of excessive power on scales of $50\hmpc$, which seems to be
inconsistent with the standard $\Lambda$CDM cosmological model. We discuss
several assumptions and conventions used in studies of the large-scale bulk
flow to check whether this claim is robust under a variety of conditions.
Rather than using a composite catalogue we select samples from the SN, ENEAR,
SFI++ and A1SN catalogues, and correct for Malmquist bias in each according to
the IRAS PSCz density field. We also use slightly different assumptions about
the small-scale velocity dispersion and the parameterisation of the matter
power spectrum when calculating the variance of the bulk flow. By combining the
likelihood of individual catalogues using a Bayesian hyper-parameter method, we
find that the joint likelihood of the amplitude parameter gives
$\sigma_8=0.65^{+0.47}_{-0.35}(\pm 1 \sigma)$, which is entirely consistent
with the $\Lambda$CDM model. In addition, the bulk flow magnitude ($v \sim 310
\kms$) and direction, $(l,b)\sim (280^{\circ} \pm 8^{\circ}, 5.1^{\circ} \pm
6^{\circ})$, found by each of the catalogues are all consistent with each
other, and with the bulk flow results from most previous studies. Furthermore,
the bulk flow velocities in different shells of the surveys constrain
$\sigma_{8}$--$\Omega_{\rm{m}}$ to be
($1.01^{+0.26}_{-0.20},0.31^{+0.28}_{-0.14}$, SFI++) and
($1.04^{+0.32}_{-0.24},0.28^{+0.30}_{-0.14}$, ENEAR), which is consistent with
{\it WMAP} 7-year best-fit values. We finally discuss the differences between
our conclusions and those of the studies claiming the largest bulk flows.
