band structure keeps growing and becomes self-sustained, indicated by the increasing kinetic energy of the flow. The flow at $t=1070$ is visualised in Figure \[fig:forcing\_amplitudes\](f), which shows a well-developed turbulent band with a head, a tail and a wave-like elongated bulk.

![\[fig:KE\_no\_noise\] [[(a) The kinetic energy of a forcing case without initial background noise. $Re=750$ and $A_x=A_z=3.0$. (b) The streamwise velocity $u_x$ (with the parabola excluded) at the center of the moving forcing area, monitored at the position of $y=-0.5$.]{}]{}](Fig6.pdf){width="80.00000%"}

![\[fig:effects\_on\_base\_flow\] The effect of the forcing on the base flow. $Re=750$ and $A_x=A_z=3.0$. (a) The maximum velocity deviation from the basic parabolic flow, $\max_y{\sqrt{(u_x-1+y^2)^2+u_y^2+u_z^2}}$, plotted in the $x-z$ plane. The black circle marks the forcing area at this time instant. [[The red line marks the level of 0.02.]{}]{} (b-d) The velocity deviation profiles at the position marked by the cyan triangle (b), by the blue cross (c) and that averaged in the forcing area (inside the black circle) (d), i.e. [[$\frac{1}{N_p}\sum{u_{x,z}(y)}$, where $N_p$ is the number of grid points that satisfy $(x-x_c)^2+(z-z_c)^2<R^2$.]{}]{}](Fig7.pdf){width="85.00000%"}

To further evidence that the turbulent band is generated by the inflectional instability, we next show the effects of the forcing on the base flow for the $A_x=A_z=3.0$ 