  We use numerical simulation of cosmological reionization to calculate the
secondary CMB anisotropies in a representative flat low density cosmological
model. We show that the kinetic Sunyaev-Zel'dovich effect (scattering off of
moving electrons in the ionized intergalactic medium) is dominated by the
nonlinear hydrodynamic and gravitational evolution of the density and velocity
fields, rather than the detailed distribution of the ionization fraction
(``patchy reionization'') on all angular scales. Combining our results with the
recent calculation of secondary CMB anisotropies by Springel et al., we are
able to accurately predict the power spectrum of the kinetic SZ effect on
almost all angular scales.
