Three-dimensional growth of quantized vortices in rotating superfluid

Makoto Tsubota, Hideki Yoneda

M. Yu. Kagan

Makoto Tsubota, Kenichi Kasamatsu

Ben McCanna, Hannah M. Price

As is well known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices, respectively. Recently, we have studied how, in a hypothetical four-dimensional (4D) superfluid, such excitations can be generalized to vortex planes and surfaces. In this paper we continue our analysis of skewed and curved vortex surfaces based on the 4D Gross-Pitaevskii equation and show that certain types of such states can be stabilized by equal-frequency double rotations for suitable parameters. This work extends the rich phenomenology of vortex surfaces in four dimensions and raises interesting questions about vortex reconnections and the competition between various vortex structures which have no direct analog in lower dimensions. Published by the American Physical Society 2024

David M. F. Chapman

The equations of motion of vortices in an ideal two-dimensional fluid are derived, and the laws of conservation associated with the motion are discussed. Two regions of flow are considered, an infinite region and a region bounded on the outside by a circle. The kinetic energy and angular momentum of a vortex fluid in these two regions are calculated. A Lagrangian formalism is introduced in order to discuss the symmetry transformations of vortex systems and their associated conservation laws. The kinematic stability of rigidly rotating polygonal configurations of quantized vortices is determined, and the states of thermodynamic equilibrium of a rotating superfluid are found for low angular velocities, resulting in the calculation of the spectrum of critical angular velocities for the creation of one, two, and three vortices.

Hiroki Saito, Masazumi Hayashi

A Rossby-Haurwitz (RH) wave is an excitation mode of a fluid on a rotating spherical surface, which propagates westward in the rotating frame of reference. Motivated by the recent realization of the shell-shaped Bose-Einstein condensate in microgravity, we investigate the RH wave in a superfluid rotating on a spherical-surface geometry. We employ the point-vortex model and the three-dimensional Gross-Pitaevskii equation, and numerically demonstrate that RH waves can be observed in the system of a superfluid with quantized vortices.