First-order velocity structure function (VSF) versus 3D separation distance for all TNG-Cluster halos at z = 0. The top row shows the VSF for small separation scales (≲10 kpc) near the cluster center (left), and larger separation scales (100 kpc < Δr_3D < 2 Mpc) in the entire cluster and its outskirts. The bottom row shows the VSF at medium separation scales (10 kpc < Δr_3D < 100 kpc) in the cluster core (bottom left), cluster intermediate regions (bottom center), and cluster outskirts (bottom right). Each color corresponds to a different halo mass bin. The thick solid lines depict the mean VSF, while the thin lines represent individual clusters. The diagonal lines correspond to the Kolmogorov slope of 1/3. Gas motion becomes less coherent with increasing separation distance, and is most coherent in the outskirts and least coherent in the cores of clusters, due to the combined effects of gravity and baryonic processes.