Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2009-09-21
Physics
Condensed Matter
Other Condensed Matter
Scientific paper
The motion of a vortex filament in superfluid 4He is considered by using the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) phenomenological model for the scattering process between the vortex and thermal excitations in liquid 4He. The HVBK equations are formulated first in the intrinsic geometric parameter space to obtain insights into the physical implications of one aspect of the friction term, associated with the friction coefficient alpha, in the Hall-Vinen notation, as well as the previous neglect of the other aspect of the friction term, associated with the friction coefficient alpha^prime. This development also serves to highlight the difficulties arising in making further progress on this route. A reformulation of the HVBK equation in the extrinsic vortex filament coordinate space is then given. This is shown to provide a useful alternative approach in this regard. A nonlinear Schrodinger equation for the propagation of nonlinear Kelvin waves on a vortex filament in a superfluid is given. The localized vortex kink solution of this equation is shown to be driven unstable by the normal fluid flow along the vortex in qualitative similarity with the Donnelly-Glaberson instability of Kelvin waves on a vortex. This instability is demonstrated in a more clear way by considering the problem of a rotating planar vortex filament in a superfluid. Furthermore, this formulation predicts an undamped one-parameter family of nonlinear Schrodinger envelope solitary waves that are totally peculiar to the superfluid vortex dynamics. Though the friction term associated with alpha, for very small alpha, has little capacity to make significant contribution to the vortex motion in a quantitative way, it is shown to be able to change the vortex motion aspects like the vortex kink characteristics in a qualitative way.
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