  We comment on the paper by Van Gorder ["Motion of a helical vortex filament
in superfluid ${}^4$He under the extrinsic form of the local induction
approximation", Phys. Fluids 25, 085101 (2013)]. We point out that the flow of
the normal fluid component parallel to the vortex will often lead into the
Donnelly-Glaberson instability, which will cause the amplification of the
Kelvin wave. We explain why the comparison to local nonlinear equation is
unreasonable, and remark that neglecting the motion in the $x$-direction is not
reasonable for a Kelvin wave with an arbitrary wave length and amplitude. The
correct equations in the general case are also derived.
