  We use hydrodynamical N-body simulations to study the kinetic
Sunyaev-Zel'dovich effect. We construct sets of maps, one square degree in
size, in three different cosmological models. We confirm earlier calculations
that on the scales studied the kinetic effect is much smaller than the thermal
(except close to the thermal null point), with an rms dispersion smaller by
about a factor five in the Rayleigh-Jeans region. We study the redshift
dependence of the rms distortion and the pixel distribution at the present
epoch. We compute the angular power spectra of the maps, including their
redshift dependence, and compare them with the thermal Sunyaev-Zel'dovich
effect and with the expected cosmic microwave background anisotropy spectrum as
well as with determinations by other authors. We correlate the kinetic effect
with the thermal effect both pixel-by-pixel and for identified thermal sources
in the maps to assess the extent to which the kinetic effect is enhanced in
locations of strong thermal signal.
