Time evolution of two successive bow shocks and the cavities predicted by the analytical model. The first bow shock is ejected at t = 0, the second shock is formed at time t = τ_j when the first bow shock is at z = v_jτ_j taken here as 6L₀ (top). At a time t = τ_j + 2L₀/v_j, the second bow shock is still propagating in the undisturbed disk wind material (center). At a time t_c the second bow shock catches up the emptied cavity of the first bow shock at its vertex (bottom).