0.001 (the resulting velocity perturbations are $\mathcal{O}(10^{-4})$. [[Note that a random noise applies equally]{}]{}). The force is switched on at $t=0$. In the following tests, we set $R=7$ and set the amplitude of the force in the streamwise and spanwise directions, i.e. $A_x$ and $A_z$, independently. Figure \[fig:forcing\_amplitudes\](a) shows the results. It can be seen that, for $A_x=3.0$, $A_z=1.0$ and 2.0 both fail to generate bands within 1200 time units, while $A_z=3.0$ succeeds (see the fast increase in the kinetic energy of disturbances after $t\simeq 300$). For $A_z=3.0$, $A_x=1.0$, 2.0 and 3.0 all successfully generate a turbulent band. The larger $A_x$ is, the earlier the turbulent band is generated. We also tested $A_x=A_z=2.0$ and found it fail to trigger a band. The results indicate that sufficiently strong forces are needed for the generation of turbulent bands and the stronger the force, the faster a band can be triggered, just as expected. The spanwise force, equivalently the spanwise velocity profile, seems to play a more important role than the streamwise one, which is consistent with our argument that the spanwise inflection plays a central role in the streak generation at the head. [[It should be noted that different velocity profiles (e.g. 