We use hydrodynamical N-body simulations to study the kinetic Sunyaev-Zel'd
ovich effect. We construct sets of maps, one square degree in size, in thre
e different cosmological models. We confirm earlier calculations that on th
e scales studied the kinetic effect is much smaller than the thermal (excep
t close to the thermal null point), with an rms dispersion smaller by about
a factor of 5 in the Rayleigh-Jeans region. We study the redshift dependen
ce of the rms distortion and the pixel distribution at the present epoch. W
e compute the angular power spectra of the maps, including their redshift d
ependence, and compare them with the thermal Sunyaev-Zel'dovich effect and
with the expected cosmic microwave background anisotropy spectrum as well a
s with determinations by other authors. We correlate the kinetic effect wit
h 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 i
n locations of strong thermal signal.