numbers in the streamwise and spanwise directions, respectively. The size of the computational domain is $L_x=2\pi/\alpha$ and $L_z=2\pi/\beta$. The finite difference scheme and the parallelisation strategy of [Openpipeflow]{} [@Willis2017], and the time-stepping and projection scheme of @Hugues1998 are employed to integrate the incompressible system.

We performed direct numerical simulations (DNS) in the regime of $Re\leqslant 750$. We considered two computational boxes with $L_x=L_z=120h$ and $L_x=L_z=320h$, respectively. For $Re=750$, we used 768 Fourier modes ($K=M=384$) in both streamwise and spanwise directions for the small box and 2048 Fourier modes ($K=M=1024$) for the large box. For $Re=600$ and 500, the number of streamwise Fourier modes is reduced to 576 for the small box and 1728 for the large box. We used 64 Chebyshev grid points for the finite difference discretisation in the wall normal direction. These resolutions were shown to be sufficient for the flow in this Reynolds number regime [@Tao2018]. A time-step size of $\Delta t=0.01$ is used for the time integration, which is sufficiently small for this Reynolds number regime.

The forcing {#sec:forcing}
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@Xiao2020 showed that turbulent bands at low Reynolds numbers grow via a streak generation mechanism at the head of the bands, i.e. an inflectional instability associated 