Evolution of the test-particle system after a large, m = 2 impact, designed with a γ correction (Eq. (6)) to excite a single spiral pattern. These panels show snapshots of the velocity field at four different times (t = 0, 0.4, 0.8, and 1.2 Gyr). The top row shows the radial velocity V_R, and the bottom row shows the residual azimuthal velocity, ∆V_ϕ = V_ϕ − V_c. The spiral pattern winds up over time at the expected rate Ω − κ/m. The large amplitude of the perturbation introduces non-linear effects, causing the regions of negative V_R (blue) to become more concentrated into arcs, and producing sharp sign changes in ∆V_ϕ. One-dimensional (1D) radial profiles extracted from these maps along ϕ = 0° (dash-dot regions) are presented in Figure 3.