Dynamics of a planar vortex filament under the quantum local induction approximation.

Area of Science:

• Quantum fluid dynamics
• Vortex dynamics
• Mathematical physics

Background:

• The Hasimoto planar vortex filament is a rare exact solution to the classical local induction approximation (LIA).
• Its stability in the absence of disturbances limits its applicability to more complex physical scenarios.
• Previous studies have not fully explored its behavior under conditions involving friction and fluid flow.

Purpose of the Study:

• To investigate the dynamics of the Hasimoto planar vortex filament under the quantum local induction approximation (LIA).
• To analyze the effects of mutual friction and normal fluid flow on the filament's stability and form.
• To extend the understanding of vortex filament behavior to more realistic physical conditions, including non-zero temperatures.

Main Methods:

• Theoretical analysis using the quantum local induction approximation (LIA).
• Inclusion of mutual friction and normal fluid velocity terms in the model.
• Analytical derivation of filament dynamics under varying conditions.
• Numerical verification of analytical results for specific physical cases.

Main Results:

• The planar vortex filament deforms over time due to mutual friction and normal fluid flow at non-zero temperatures.
• Mutual friction induces torsion, causing the filament to bend as it rotates.
• Normal fluid flow leads to spatial growth of initial planar perturbations along the filament.
• The magnitude of these deformation effects scales with the mutual friction coefficient, increasing at warmer temperatures.

Conclusions:

• The stability of the Hasimoto planar vortex filament is compromised by quantum effects, specifically mutual friction and normal fluid flow.
• Temperature plays a critical role, with warmer conditions amplifying the observed deformations.
• The study provides analytical and numerical insights into the complex dynamics of vortex filaments in realistic physical environments.