Comment on 'Motion of a helical vortex filament in superfluid ~4He under the extrinsic form of the local induction approximation' [Phys. Fluids 25, 085101 (2013)]

摘要

We comment on the paper by Van Gorder ["Motion of a helical vortex filament in superfluid ~4He 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 wavelength and amplitude. The correct equations in the general case are also derived.