  We study a geometric flow on curves, immersed in $\mathbb{R}^3$, that have
strictly positive torsion. The evolution equation is given by
$$X_{t}=\frac{1}{\sqrt{\tau}} \textbf{B}$$ where $\tau$ is the torsion and
$\textbf{B}$ is the unit binormal vector. In the case of constant curvature, we
find all of the stationary solutions and linearize the PDE for torsion around
stationary solutions admitting an explicit formula. Afterwards, we prove the
$L^2(\mathbb{R})$ linear stability of the stationary solutions corresponding to
helices with constant curvature and constant torsion.
