  One of the most promising ways to study the epoch of reionization (EoR) is
through radio observations of the redshifted 21-cm line emission from neutral
hydrogen. These observations are complicated by the fact that the mapping of
redshifts to line-of-sight positions is distorted by the peculiar velocities of
the gas. Such distortions can be a source of error if they are not properly
understood, but they also encode information about cosmology and astrophysics.
We study the effects of redshift space distortions on the power spectrum of
21-cm radiation from the EoR using large scale $N$-body and radiative transfer
simulations. We quantify the anisotropy introduced in the 21-cm power spectrum
by redshift space distortions and show how it evolves as reionization
progresses and how it relates to the underlying physics. We go on to study the
effects of redshift space distortions on LOFAR observations, taking instrument
noise and foreground subtraction into account. We find that LOFAR should be
able to directly observe the power spectrum anisotropy due to redshift space
distortions at spatial scales around $k \sim 0.1$ Mpc$^{-1}$ after $\gtrsim$
1000 hours of integration time. At larger scales, sample errors become a
limiting factor, while at smaller scales detector noise and foregrounds make
the extraction of the signal problematic. Finally, we show how the
astrophysical information contained in the evolution of the anisotropy of the
21-cm power spectrum can be extracted from LOFAR observations, and how it can
be used to distinguish between different reionization scenarios.
