Kinematic maps comparing the evolution of velocity fields in the N-body (first and third columns) and TPR models (second and fourth columns). The panels show snapshots of the radial velocity V_R (top row) and the azimuthal velocity perturbation ∆V_ϕ (bottom row) in the X–Y plane at two different times. The dashed circle denotes the inner region (R < 7 kpc) that was excluded from the analysis. Observe the winding of the spiral patterns over time and the overall similarity between the N-body and TPR models, with subtle differences, particularly in the amplitude of the kinematic waves.