Vortex dynamics in the two-fluid model (original) (raw)
Related papers
Annals of Physics, 2014
We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov's hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov's action, which, in particular, allows for weak solutions of the Gross-Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.
Particles and fields in superfluids: Insights from the two-dimensional Gross-Pitaevskii equation
Physical Review A
We carry out extensive direct numerical simulations (DNSs) to investigate the interaction of active particles and fields in the two-dimensional (2D) Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; and (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid Helium and Bose-Einstein condensates.
2014
Owing to three conditions (namely: (a) the velocity is represented by sum of irrotational and solenoidal components; (b) the fluid is barotropic; (c) a bath with the fluid undergoes vertical vibrations) the Navier-Stokes equation admits reduction to the modified Hamilton-Jacobi equation. The modification term is the Bohmian(quantum) potential. This reduction opens possibility to define a complex-valued function, named the wave function, which is a solution of the Schrödinger equation. The solenoidal component being added to the momentum operator poses itself as a vector potential by analogy with the magnetic vector potential. The vector potential is represented by the solenoidal velocity multiplied by mass of the fluid element. Vortex tubes, rings, and balls along with the wave function guiding these objects are solutions of this equation. Motion of the vortex balls along the Bohmian trajectories gives a model of droplets moving on the fluid surface. A peculiar fluid is the superfluid physical vacuum. It contains Bose particle-antiparticle pairs. Vortex lines presented by electron-positron pairs are main torque objects. Bundles of the vortex lines can transmit a torque from one rotating disk to other unmoved disk.
Dissipative dynamics of vortex lines in superfluid â´He
Physical Review B, 1997
We propose a Hamiltonian model that describes the interaction between a vortex line in superfluid 4^{4}4He and the gas of elementary excitations. An equation of irreversible motion for the density operator of the vortex, regarded as a macroscopic quantum particle with a finite mass, is derived in the frame of Generalized Master Equations. This enables us to cast the effect of the coupling as a drag force with one reactive and one dissipative component, in agreement with the assumption of the phenomenological theories of vortex mutual friction in the two fluid model.
A topological defect model of superfluid vortices
Physica D: Nonlinear Phenomena, 1996
This paper introduces a nonlinear Schrrdinger model for superfluid that captures the process of mutual friction between the superfluid and normal fluid components of helium II. Superfluid vortices are identified as topological defects in the solution of this equation. A matched asymptotic analysis of Neu is adapted to derive an asymptotic dynamics for the vortices in the case they are widely separated compared with their core size. This motion agrees with the classical Hall and Vinen motion in which phenomenological drag terms are added, ad hoc, to the motion of vortices in an inviscid fluid. Several simple examples are considered to illustrate the unique character of the motion of superfluid vortices. Finally, the motion of vortices in uniformly rotating helium II is considered, and a continuum approximation to their dynamics is obtained in the case of very many vortices.
Superfluidity and vortices: A Ginzburg-Landau model
The paper deals with the study of superfluidity by a Ginzburg-Landau model that investigates the material by a second order phase transition, in which any particle has simultaneouly a normal and superfluid motion. This pattern is able to describe the classical effects of superfluidity as the phase diagram, the vortices, the second sound and the thermomechanical effect. Finally, the vorticities and turbulence are described by an extension of the model in which the material time derivative is used.
Hydrodynamic equations of anisotropic, polarized and inhomogeneous superfluid vortex tangles
Physica D: Nonlinear Phenomena, 2011
We include the effects of anisotropy and polarization in the hydrodynamics of inhomogeneous vortex tangles, thus generalizing the well known Hall-Vinen-Bekarevich-Khalatnikov equations, which do not take them in consideration. These effects contribute to the mutual friction force F ns between normal and superfluid components and to the vortex tension force ρ s T. These equations are complemented by an evolution equation for the vortex line density, which takes into account these contributions.