Knowledge about the cosmic velocity field is crucial in understanding various aspects in large scale structure formation. Its statistics help modelling distortions in redshift space and interpreting measurements of the kinetic Sunyaev-Zeldovich effect. In standard perturbation theory (SPT) one usually looks at the velocity divergence, since the rotational part decays in the linear regime proportional to the scale factor. In N-body simulations the statistics of the three dimensional field can be measured, but may be prone to low resolution difficulties in low density regions. Based on a kinetic field theory ansatz developed by Bartelmann et al. (2016), I will present a way to assess the statistics of the 3D velocity field and results for the power spectra of the kinetic energy density, velocity divergence, and vorticity field including non-linear scales.