a) Spacecraft crossing an expanding circular flux rope. The spacecraft trajectory is drawn by a straight thin line, the boundary of the cloud/rope at the spacecraft entry (leading boundary) is the solid-line circle, the boundary at the spacecraft exit (trailing boundary) is the dashed-line circle. The bullet indicates the position of the rope axis. b) The ambient solar wind and expansion (V_r) velocities add at the leading boundary and subtract at the trailing one, which results in a decrease in observed velocity magnitude; the vertical lines indicate the flux rope boundaries, and their line types match the ones in panel a). c) Radial velocity V_r is highest near the boundary and drops to zero at the axis. It yields a characteristic “U” shape profile in the modeled V_r.