Schematic diagram of the flow around an internal working surface (IWS) in the frame of reference co-moving with the IWS at velocity v_z = v_j (a similar configuration would apply for the leading working surface of a jet). The thick, horizontal line at the bottom of the graph is the jet (with a gap showing the position of the IWS). The working surface ejects jet material sideways at an initial velocity v₀ into the slower disk wind, which in this frame of reference moves towards the outflow source at velocity v_j – v_w. The distance x is measured towards the outflow source.The shape of the thin shell bow shock is given by r_b(x) (see Eq. (5)), and terminates at the cylindrical radius r_{b; f}(t) with t the time elapsed since formation of the IWS (see Eq. (8)).