case. To allow the base flow to develop sufficiently before the transition occurs, we performed a simulation without initial background noise, see Figure \[fig:KE\_no\_noise\] and \[fig:effects\_on\_base\_flow\]. Comparing with the case with background noise (Figure \[fig:forcing\_amplitudes\](a)), it takes approximately twice the time, roughly 600 time units, for the transition to occur. At $t=400$, at which the base flow seems to have stabilised under the forcing, we plotted the maximum velocity deviation with respect to the parabolic flow in the $x-z$ plane, see figure \[fig:effects\_on\_base\_flow\](a), in which the forcing area is moving downward and to the right, and the black circle in the figure marks the forcing area at this time instant. Large velocity deviation is seen in the upper half and right shoulder of the forcing area. Although the velocity deviation is not limited in the forcing area, the region that the force significantly affects is not much larger than the forcing area [[(see the level of 0.02 marked in the figure)]{}]{}, which means that the effect of the force is sufficiently localised and does not significantly influence the bulk and tail of the generated turbulent band. Panels (b) and (c) show the velocity profiles at the position of $(x,z)=(65,65)$ (marked 