(a) Nobeyama 45m H¹³CO⁺ (1–0) and C¹⁸O (1–0) centroid velocities along the filament, (b) NOEMA+45m H¹³CO⁺ (1–0) centroid velocities along the filament, and (c) Nobeyama 45m H¹³ CO⁺ (1–0) and C¹⁸O (1–0) centroid velocities along the r direction. In each panel, blue and red points indicate the centroid velocity of H¹³ CO⁺ and C¹⁸ O, respectively. In panels a and b, the blue and red curves show the result of the least square fitting with a function of υ(z) = V_sys + z∇V_z + V₀ cos(2πz/λ + θ_offset) against the H¹³CO⁺ (1–0) and C¹⁸O(1–0) centroid velocity. In panels a and b, the black curves indicate the distribution of Herschel H₂ column density along the filament in the 25″ resolution map. The vertical gray strips indicate the positions of Herschel dense cores identified by Könyves et al. (2020, HGBS 054203.2-020235, 054157.3-020101, 054153.4-020016, and 054149.5-015941). The width of each strip corresponds to a 25″ beam. The core labeled in green is associated with a Spitzer protostar (Megeath et al. 2012). In this plot, z measures the position along the magenta curve in Fig. 1, and z = 0 corresponds to the southeastern edge of the curve. Each data point is on the crest of the filament. In panel c, the two solid and dashed lines show the best-fit transverse velocity gradient of the form V(r) = V_sys + r∇V_r observed in H¹³CO⁺ (1–0) and C¹⁸O (1–0), respectively. r = 0 corresponds to the crest of the filament as indicated by the magenta curve in Fig. 1. All pixels in the maps of Figs. 7a, b, and d are used for this plot by estimating the projected separation from the filament crest.