fully localised turbulent bands at low Reynolds numbers, @Shimizu2019 [@Kanazawa2018] observed that turbulent bands are sustained by an active streak-generating downstream end (hereafter referred to as head). @Kanazawa2018 considered a damped Navier-Stokes system and proposed that a relative periodic orbit seems to exist at the head and is responsible for the self-sustainment of the band. @Xiao2020 lately investigated the local mean flow at the head of turbulent bands at $Re=750$ and showed that the spanwise velocity profile manifests a strong inflection. They performed linear stability analysis of the inflectional profile and found a linear instability. The most unstable eigenmode as well as the nonlinear development of perturbations on top of the inflectional velocity profile showed remarkable similarities with the wave-like streaky structure observed at the head of turbulent bands. They also showed that streaks decay continually at the upstream end of turbulent bands (hereafter referred to as tail). Therefore, they proposed that the growth of fully localised turbulent bands are driven by the instability associated with the inflectional local mean flow at the head. Similar mechanisms were proposed for the growth mechanism of the wing tips of turbulent spots at higher Reynolds numbers in channel flow [@Henningson1987; @Henningson1989], in plane 