Hydrodynamic Boundary Conditions in Superfluids (original) (raw)

Simulating infinite vortex lattices in superfluids

We present an efficient framework to numerically treat infinite periodic vortex lattices in rotating superfluids described by the Gross-Pitaevskii theory. The commonly used split-step Fourier (SSF) spectral methods are inapplicable to such systems as the standard Fourier transform does not respect the boundary conditions mandated by the magnetic translation group. We present a generalisation of the SSF method which incorporates the correct boundary conditions by employing the so-called magnetic Fourier transform. We test the method and show that it reduces to known results in the lowest-Landau-level regime. While we focus on rotating scalar superfluids for simplicity, the framework can be naturally extended to treat multicomponent systems and systems under more general 'synthetic' gauge fields.

Numerical Simulations of Superfluid Turbulence under Periodic Conditions

Journal of Low Temperature Physics, 2007

This paper is devoted to numerical simulation of vortex tangle dynamics in superfluid helium. The problem is solved on the base of the so called reconnection ansatz consisting of the equation of motion for vortex lines plus reconnection of a loop. A new algorithm, which is based on consideration of crossing lines, is used for the reconnection processes. Calculations are performed for a cubic box. Periodic boundary conditions are applied in all directions. We use the 4th order Runge-Kutta method for the integrations in time. The dynamics of quantized vortices with various counterflow velocities is studied. The density of vortex lines and number of reconnections as functions of vortex line density are calculated.

A vortex filament tracking method for the Gross–Pitaevskii model of a superfluid

Journal of Physics A: Mathematical and Theoretical, 2016

We present an accurate and robust numerical method to track quantized vortex lines in a superfluid described by the Gross-Pitaevskii equation. By utilizing the pseudovorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a-priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems.

Superfluid vortex lines in a model of turbulent flow

Physics of Fluids, 1997

Recent experiments have shown that the high Reynolds number turbulent flow of superfluid helium is similar to classical turbulence. To understand this evidence we have developed an idealized model of normal fluid turbulence which is based on vorticity tubes and we have studied numerically the behavior of superfluid quantized vortex lines in this model of turbulent normal flow. We have found that the vortex lines form ordered superfluid vortex bundles in regions of high normal fluid vorticity. A vortex wave instability and mutual friction are responsible for generating a high density of vortex lines such that the resulting macroscopic superfluid vorticity and the driving normal fluid vorticity patterns match. The results are discussed from the point of view of the idea, put forward to explain experiments, that in the isothermal, turbulent flow of He II a high density of vortex lines locks the two fluid components together and the resulting turbulent flow is that of a classical Navier-Stokes fluid.

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.

Equation for self-consistent superfluid vortex line dynamics

2000

Turbulence in helium II takes the form of a disordered tangle of quantised vortex line. The existing equation of vortex dynamics used by Schwarz and others to model the evolution of the vortex tangle does not distinguish between the large scale normal fluid velocity and the local variation of the normal fluid velocity introduced by the presence of quantised vortex lines. We derive a new vortex dynamics equation which allows the local normal fluid velocity to be determined by a modified Navier Stokes equation. Together, the two equations form a self-consistent model to determine the coupled evolution of the normal fluid and quantised vortices.

Phase Transitions Driven by Vortices in 2D Superfluids and Superconductors

The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the parameter λ which multiplies the quartic term (it turns out that this is equivalent to consider different values of the coherence length ξ in units of the lattice spacing a). It is observed that amplitude fluctuations can change dramatically the nature of the phase transition: for small values of λ (ξ/a > 0.7) , instead of the smooth Kosterlitz-Thouless transition there is a first order transition with a discontinuous jump in the vortex density v and a larger non-universal drop in the helicity modulus. In particular, for λ sufficiently small (ξ/a ∼ = 1) , the density of bound pairs of vortex-antivortex below Tc is so low that, v drops to zero almost for all temperature T < T c.

Hidden vortex lattices in a thermally paired superfluid

We study the evolution of rotational response of a hydrodynamic model of a two-component superfluid with a non-dissipative drag interaction, as the system undergoes a transition into a paired phase at finite temperature. The transition manifests itself in a change of (i) vortex lattice symmetry, and (ii) nature of vortex state. Instead of a vortex lattice, the system forms a highly disordered tangle which constantly undergoes merger and reconnecting processes involving different types of vortices, with a "hidden" breakdown of translational symmetry.

Exotic Vortex Lattices in Binary Repulsive Superfluids

Physical Review Letters

We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m1 = m2. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case m2/m1 = 2 and list a number of geometries that are found for higher integer mass ratios.

Scattering of Line-Ring Vortices in a Superfluid

Journal of Low Temperature Physics, 2015

We study the scattering of vortex rings by a superfluid line vortex using the Gross-Pitaevskii equation in a parameter regime where a hydrodynamic description based on a vortex filament approximation is applicable. By using a vortex extraction algorithm, we are able to track the location of the vortex ring as a function of time. Using this, we show that the scattering of the vortex ring in our Gross-Pitaevskii simulations is well captured by the local induction approximation of a vortex filament model for a wide range of impact parameters. The scattering of a vortex ring by a line vortex is characterised by the initial offset of the centre of the ring from the axis of the vortex. We find that a strong asymmetry exists in the scattering of a ring as a function of this initial scattering parameter.