Non-linearities (NL) modeled by the BORG dynamical model. Left panel: relative difference between the velocity field derived from the gravity field assuming linearity and the non-linear velocity field produced by BORG with respect to the total for the ensemble mean fields. Right panel: standard deviation of the velocity field for each density bin (orange curve) and standard deviation of the non-linear velocity, (v_r, BORG − v_r, linear), for each density bin (blue curve). We see here that the non-virial, non-linear component of the velocity field can represent a substantial portion of the cosmic velocity field: up to ∼25% of the standard deviation of the total velocity field when the local matter density exceeds δ_m ≳ 4.