A hydrodynamic approach to reproduce multiple spinning vortices in horizontally rotating three-dimensional liquid helium-4

TL;DR

This paper presents a 3D simulation method for rotating liquid helium-4 using a two-fluid model and SPH, successfully reproducing multiple spinning vortices and advancing the simulation techniques for quantum fluids.

Contribution

The study introduces a large-scale, high-resolution SPH simulation of rotating liquid helium-4 that captures vortex formation, based on a novel two-fluid model with spin-angular momentum conservation.

Findings

High-resolution simulation with 19.6 million particles accurately reproduces vortex structures.

The model demonstrates consistency with conventional two-fluid theory.

Simulation results align closely with theoretical vortex solutions.

Abstract

This paper reports a three-dimensional (3D) simulation of a rotating liquid helium-4, using a two-fluid model with spin-angular momentum conservation. Our model was derived from the particle approximation of an inviscid fluid with residual viscosity. Despite the fully classical mechanical picture, the resulting system equations were consistent with those of the conventional two-fluid model. We consider bulk liquid helium-4 to be an inviscid fluid, assuming that the viscous fluid component remains at finite temperatures. As the temperature decreased, the amount of the viscous fluid component decreased, ultimately becoming a fully inviscid fluid at absolute zero. Weak compressibility is assumed to express the volume change because some helium atoms do not render fluid owing to BECs or change states because of local thermal excitation. One can solve the governing equations for an incompressible fluid using explicit SPH (smoothed particle hydrodynamics), simultaneously reproducing density fluctuations and describing the fluid in a many-particle system. We assume the following fluid-particle duality: a hydrodynamic interfacial tension between the inviscid and viscous components or a local interaction force between two types of fluid particles. The former can be induced in the horizontal direction when non-negligible non-uniformity of the particles occurs during forced two-dimensional rotation, and the latter is non-negligible when the former is negligible. We performed a largescale simulation of 3D liquid helium forced to rotate horizontally using 32 GPUs. Compared with the low-resolution calculation using 2.4 million particles, the high-resolution calculation using 19.6 million particles showed spinning vortices close to those of the theoretical solution. We obtained a promising venue to establish a practical simulation method for bulk liquid helium-4.