orientation of the generated bands.

Methods
=======

The non-dimensional incompressible Navier-Stokes equations $$\label{equ:NS}
 \frac{\partial \bm u}{\partial t}+{\bm u}\cdot\bm{\nabla}
{\bm u}=-{\bm{\nabla}p}+\frac{1}{Re}{\bm\nabla^2}{\bm u} + {\bm F}, \;
\bm{\nabla}\cdot{\bm u}=0$$ with a constant volume flux for the channel geometry are solved in Cartesian coordinates $(x, y, z)$, where $\bm u$ denotes velocity, $p$ denotes pressure, $\bm F$ denotes the external force and $x$, $y$ and $z$ represent the streamwise, wall-normal and spanwise coordinates, respectively. Velocities are normalized by $U_c$, length by $h$ and time by $h/U_c$. [[For all simulations in this paper, the volume flux associated with the unperturbed parabolic flow is imposed.]{}]{} No-slip boundary conditions for velocities are imposed at channel walls (i.e. at $y=\pm 1$). Periodic boundary conditions are imposed in the streamwise and spanwise directions. A hybrid Fourier spectral-finite difference method is used to solve Eqs. (\[equ:NS\]), with a finite-difference method with a 9-point stencil employed for the discretisation in the wall normal direction. Therefore, the velocity and pressure fields can be expressed as $${A}(x,y,z,t)=\sum_{k=-K}^{K}\sum_{m=-M}^{M}\hat{A}_{k,m}(y,t)e^{i(\alpha kx+\beta mz)},$$ where $k$ and $m$ are the indices of the streamwise and spanwise Fourier modes, respectively, $\hat A_{k,m}$ is the Fourier coefficient of the mode $(k,m)$ and $\alpha$ and $\beta$ are the fundamental wave 