with the local mean flow. Inspired by their study, here we aim to generate banded streaks, as those observed in turbulent bands, via such an instability mechanism. We propose to impose a body force that locally induces a spanwise inflectional velocity profile. We first design a target streamwise and spanwise velocity profile that is inflectionally unstable, and subsequently derive the force that can generate the profile. [[We use polynomial fits of the velocity profiles that @Xiao2020 measured at the head of a turbulent band at $Re=750$, with the parabola $1-y^2$ subtracted from the streamwise component. The profiles read]{}]{} $$\begin{aligned}
\label{equ:target_profile}
U_x&=&-0.2478y^8 + 0.5390y^6 -0.2768y^4-0.1250y^2+0.1106, \\
\label{equ:target_profile_2}
U_z&=&-0.2469y^8 + 0.7262y^6 -0.8448y^4+0.3765y^2-0.0110, \end{aligned}$$ and Figure \[fig:target\_profiles\](a) shows the $y$-dependence of the profiles. We derive the force $\boldsymbol f$ [[that is needed to maintain the profile]{}]{} as a function of $y$ as $$\label{equ:forcing}
{\boldsymbol f}+\frac{1}{Re}\nabla^2 \boldsymbol U=0,$$ [[where $\boldsymbol U=(U_x, 0, U_z)$. It should be noted that the force given by (\[equ:forcing\]) is meant to generate velocity deviations $(U_x, 0, U_z)$ with respect to the parabola $1-y^2$. Figure \[fig:target\_profiles\](b) shows the force determined by the target profiles.]{}]{}

![\[fig:target\_profiles\] (a) The velocity profiles (\[equ:target\_profile\]) (\[equ:target\_profile\_2\]). (b) The forces that are determined by (\[equ:forcing\]) using 