Maps of disc vertical velocity υ_z. Top panels: υ_z,sim/c_s velocity field from the simulation (top left panel) compared to the theoretical model υ_z,th/c_s obtained solving Eq. (29) (top right panel). Bottom panels: residuals of the simulation against the theoretical model (υ_z,sim − υ_z,th)/c_s (bottom left panel), i.e. the top left panel minus the top right panel of this figure, and with respect to a circular disc (υ_z,sim − υ_z,circ)/c_s (bottom right panel), i.e. υ_z,circ = 0; this last plot is in fact the same as top left panel but with rescaled colourbar for a direct comparison with the other residuals plot in the bottom left panel. We note that in the simulation the m = 1 spiral shaped vertical velocity feature standing out even after the subtraction of the eccentric theoretical model suggests that some additional physical processes are affecting the disc dynamics.