different $A_x$ and $A_z$ result in different velocity profiles) can be used to trigger instabilities and generate turbulent bands, as long as the profiles bear proper inflectional instability.]{}]{}

For the case of $A_x=A_z=3.0$, we switched off the forcing at $t=550$ and the band generated by the forcing continues to grow, as indicated by the growing kinetic energy of the velocity field in Figure \[fig:forcing\_amplitudes\](b). This indicates that the band generated by the forcing can be self-sustained even if the forcing is deactivated. Figure \[fig:forcing\_amplitudes\](c-e) visualises the development of the flow under the forcing. We can see the locally deformed flow (see the yellow spot) at $t=200$ in panel (c). At $t=400$, tilted wavy structures (alternating high- and low-speed streaks) are generated by the instability of the forced local flow (see panel (d)) and the kinetic energy monotonically grows as more wavy streaks are generated. At $t=550$, a short band structure is generated with a streak-generating head at the downstream end (the right-bottom end) and a rather weak tail at the upstream end (the left-top end), which are the key characteristics of a turbulent band in channel flow at low Reynolds numbers [@Tao2018; @Shimizu2019; @Kanazawa2018]. After the force is deactivated, the 