We investigate the effect of peculiar velocities on the redshift space distribution of z>~2 galaxies, and we focus in particular on Ly-alpha emitters. We generate catalogues of dark matter (DM) halos and identify emitters with halos of the same co-moving space density (M(Ly-alpha emitters) ~ 3x10^11 M_sun). We decompose the peculiar velocity field of halos into streaming, gradient and random components, and compute and analyse these as a function of scale. Streaming velocities are determined by fluctuations on very large scales, strongly affected by sample variance, but have a modest impact on the interpretation of observations. Gradient velocities are the most important as they distort structures in redshift space, changing the thickness and orientation of sheets and filaments. Random velocities are typically below or of the same order as the typical observational uncertainty on the redshift. We discuss the importance of these effects for the interpretation of data on the large-scale structure as traced by Ly-alpha emitters (or similar kinds of astrophysical high-redshift objects), focusing on the induced errors in the viewing angles of filaments. We compare our predictions of velocity patterns for Ly-alpha emitters to observations and find that redshift clumping of Ly-alpha emitters, as reported for instance in the fields of high-redshift radio galaxies, does not allow to infer whether an observed field is sampling an early galaxy overdensity.
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