perturbation energy is amplified by nearly 100 times, suggesting an Orr-mechanism. After $t\simeq 30$ the flow roughly takes the form of the most unstable mode that amplifies exponentially at later times (see panel (d) and panel (a)). The results indicate that small disturbances may achieve a large amplification of roughly 200 times within a short time via the Orr-mechanism and subsequently amplify exponentially due to the underlying modal instability. Jointly, these linear mechanisms can result in a fast and large energy growth of nearly 1000 times within about 60 time units (see Figure \[fig:non\_modal\_most\_unstable\](a)).

These properties of the spanwise inflectional velocity profile are very likely responsible for the fast streak generation at the head of turbulent bands at low Reynolds numbers. We use such velocity profiles to derive the force in order to induce local velocity profiles of similar stability properties and consequently trigger turbulent bands.

Generation of a single band
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Sustained-band regime
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Here we show results at $Re=750$, which is in the regime of sustained turbulent band [@Tao2018; @Kanazawa2018; @Shimizu2019]. According to @Xiao2020, the head of a turbulent band at Re=750 travels at the speeds of $c_z=0.1$ (in absolute value) and $c_x=0.85$. Therefore, to mimic a moving 