Reproduction of vortex lattices in the simulations of rotating liquid helium-4 by numerically solving the two-fluid model using smoothed-particle hydrodynamics incorporating vortex dynamics

Abstract

Our recent study has shown that the representative phenomena of liquid helium-4 rotating in a cylinder could be simulated by solving the two-fluid model using smoothed-particle hydrodynamics (SPH) after reformulating the viscosity to conserve the rotational angular momentum. Specifically, the emergence of multiple parallel vortices and their rigid-body rotations were observed in our previous SPH simulations. The reported scheme is based on a classical approximation that assumes the fluid forces of both components and their interactions, with the expectation of functioning as a coarse-grained model of existing approximations that couple a microscopic model and the Navier–Stokes equation. Based on previous studies, this paper proposes an improved SPH scheme that explicitly incorporates vortex dynamics into SPH to reproduce vortex lattices, which was not possible in previous studies. Consequently, our improved scheme was observed to reproduce vortex lattices by introducing the Magnus force and interaction forces among vortices into the reformulated two-fluid model. The spinning of the vortices and rigid-body rotations were also observed. The number of vortices showed a certain agreement with Feynman's rule after the model parameter was optimized. Notably, from a scientific point of view, such vortex lattices are reproduced by the classical-mechanical approximation. We hope that our model will help physicists studying low-temperature physics find a new way of approaching this bizarre phenomenon that has attracted attention for more than 80 years.

Three-dimensional analysis of vortex-lattice formation in rotating Bose–Einstein condensates using smoothed-particle hydrodynamics

“…Therefore, we expect that the microscopic interactions among atomic particles can be replicated more accurately using analytical particles in the simulation domain. In addition, our recent study showed that the SPH simulation of the angular momentum-conserving two-fluid model incorporating vortex dynamics reproduces vortex lattices [13]. Our another study provided a theory that the equation of motion for inviscid fluids in the two-fluid model becomes equal to the quantum hydrodynamic equation derived from the GP equation under specific conditions in SPH form [6].…”

“…At higher resolutions, our SPH scheme may help find the analytical solution of a point-vortex model for the spatial geometry of vortex lattices in 3D cases by exploring the behavior of ghost vortex lines in the vertical direction, similar to the 2D cases [23]. It may also be possible to compare the vortex lattice of the GP equation with that reproduced by a two-fluid model [13] to find a connection in the SPH form. In addition, figure 9 shows the velocity vectors of the condensates on the crosssection at z = 0.…”