## Vortex Motion in Superfluid $^4$He: Effects of Normal Fluid Flow

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Shivamoggi, Bhimsen K.

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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 analytically formulated first in the intrinsic geometric
parameter space to obtain insights into the physical implications of the
friction terms, associated with the friction coefficients alpha and alpha^prime
(in the Hall-Vinen notation) as well as the previous neglect of the friction
term associated with the friction coefficient alpha^prime. The normal fluid
velocity components both along and transverse to the vortex filament are
included. This analytical 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 which
is known (Shivamoggi) to provide a useful alternative analytical approach in
this regard. A nonlinear Schrodinger equation for the propagation of nonlinear
Kelvin waves on a vortex filament in a superfluid is given taking into account
the generalized normal fluid flow. The friction term associated with
alpha^prime, even in the presence of the normal fluid velocity components
transverse to the vortex filament, is shown to produce merely an algebraic
growth of the Kelvin waves hence providing further justification for the
neglect of this term. On the other hand, the instability produced by the
friction term associated with alpha via the normal fluid velocity component
along the vortex filament is shown to manifest itself as a parametric
amplification on considering the problem of a rotating planar vortex filament
in a superfluid.

##### Keywords

Condensed Matter - Other Condensed Matter