Second-order effects of smoothed velocity fields in N-body simulations

Weakly nonlinear effects of velocity fields obtained from N-body data are s tudied perturbatively. These numerical fields are usually smoothed in a mas s-weighted manner, in contrast to analytical predictions that are based on volume-weighted smoothing. We analyze a two-step Gaussian smoothing method using the framework of second-order perturbation theory. We also derive sec ond-order corrections caused by an adaptive filtering. With these expressio ns, artificial effects of filtering on the statistical analysis of smoothed velocity fields are discussed quantitatively.