of magnitude smaller than that associated with the generated turbulence. Therefore, the turbulent band is not directly fed by the force, instead, by the instability of the local flow induced by the force, see the wave-like streaks in Figure \[fig:forcing\_amplitudes\](c-e), which locally resemble the unstable waves shown in the linear analysis (Figure \[fig:unstable\_region\_and\_nonmodal\_growth\](b)).

![\[fig:different\_deactivation\] [[The effects of different deactivation of the force on the flow at $Re=750$. (a) The strength function of the sharp deactivation (thin red) and gradual deactivation (green) of the force tested in our study. (b) Deactivate the force according to (a) before the transition to turbulence occurs. (c) The streamwise velocity at the center of the forcing area in the simulations shown in (b). In panels (b,c), the bold black lines are taken from Figure \[fig:KE\_no\_noise\](a,b) and the sharp deactivation is at $t=400$. (d) Deactivate the force after the transition to turbulence occurs. The bold black line is the same as the one in Figure \[fig:forcing\_amplitudes\](b). Note that the deactivation in (d) is the same as that in (b, c) except for a 150-time-unit delay (the sharp one is at $t=550$).]{}]{}](Fig8.pdf){width="90.00000%"}

[[In the results shown before, the force is turned off sharply. We also studied the 