by a cyan triangle in panel (a)), where the largest deviation is located, and at the center of the forcing area $(x,z)=(60, 60)$ (marked by a blue cross in panel (a)), respectively. Panel (d) shows the velocity profile averaged over $x$ and $z$ directions within the forcing area. Clearly, the force generates significant inflection in the local velocity profiles, which qualitatively resemble the velocity profile shown in Figure \[fig:target\_profiles\]. It should be noted that the forcing itself does not bring in turbulent fluctuations, see the stationary kinetic energy between $t=200$ and 600 in Figure \[fig:KE\_no\_noise\](a) and the nearly constant streamwise velocity at the center of the moving forcing area shown in panel (b). Besides, the magnitude of the velocity deviation induced by the force is much smaller than that of turbulent fluctuations inside turbulent bands. Figure \[fig:effects\_on\_base\_flow\] shows that the former is overall smaller than 0.1, whereas the maximum of the latter is no less than 0.3 in the cut plane at $y=-0.5$, see Figure \[fig:forcing\_amplitudes\](d-e), and can be as large as around 0.5 in the whole domain, see Figure \[fig:compare\_structure\_Re600\_750\](b,c). Roughly, it can be estimated that the kinetic energy density directly injected by the force is roughly one order 