Shiran Bao

Classical viscous rings can tilt and deform through vorticity redistribution within finite cores. A quantized ring in superfluid helium lacks this pathway, leaving its response to controlled shear under two-way coupling unclear. We simulate a ring in sheared thermal counterflow. Migration and ring-plane rotation reverse with the imposed gradient and vary approximately with its strength. At T=1.65 K and Lx=Ly=1.0 mm, the dissipative α term contributes most to migration, whereas background-superflow advection contributes most to rotation. Similar reorientation of classical and quantized rings therefore need not share the same physical origin.

Thermal counterflow of superfluid He 4 past a cylinder produces quasisteady eddies not only downstream but also anomalously upstream. However, the mechanism and organizing principles behind the observed multistable wake topologies (zero-, two-, four-, and six-vortex states) have remained unclear. We show that the full spectrum of reported normal-fluid wake states is captured numerically with a two-fluid model coupled to Vinen’s vortex-line-density equation. Our simulations further reveal that the superfluid component can also develop anomalous upstream eddies, a feature not previously reported. We trace these behaviors to a self-organized zone of enhanced mutual-friction dissipation near the cylinder shoulders that reshapes the effective obstacle, drives upstream eddies in both components, and suppresses intrinsic wake oscillations in the normal fluid. Guided by this mechanism, we perform systematic parameter scans and construct a unified phase diagram in terms of the normal-fluid Reynolds number Re n and a dimensionless interaction number N , separating inertia- and mutual-friction-controlled transitions and delineating the parameter windows for the discrete wake topologies. These results turn a striking phenomenology into a predictive map and establish mutual-friction feedback as a robust route to unusual wake structures in quantum fluids.

Simulating individual quantized vortices in superfluid helium in the presence of localized boundaries presents significant computational challenges. This paper develops a finite-volume method (FVM) implementation based on Open-source Field Operation And Manipulation for existing mesoscopic vortex-filament coupling formulations in spatially non-uniform fields. The solver incorporates the one-way vortex filament method, the traditional two-way (2W) coupling model, and the fully self-consistent two-way formulation within a unified Eulerian–Lagrangian workflow. Leveraging the geometric versatility of the FVM, the implementation accommodates complex non-conformal boundaries and synthesizes mass-conserving background potential flows. To improve the numerical robustness of the Lagrangian filament evolution without artificial geometric shrinkage, we integrate a Taubin λ−μ smoothing algorithm for spatial regularization. After benchmarking algorithmic fidelity against the intrinsic decay of bare and particle-decorated vortex rings, we investigate the symmetry-breaking kinematics of a single vortex traversing a localized thermal counterflow. Numerical results reveal that macroscopic spatial shear imposes an asymmetric mutual friction distribution on the vortex. This differential drag induces unequal descent velocities across the filament, tilting the orbital plane of the ring. The resulting reorientation of the self-induced velocity overcomes the local background superfluid advection, driving a continuous lateral drift that achieves a transverse displacement of 0.186 mm within 0.5 s. A mutual-friction dissipation analysis shows that this non-uniform trajectory reduces the length-normalized dissipation rate by 55.1% and the accumulated mutual-friction work by 30.4% relative to the uniform-counterflow case.

The entrance effect in the thermal counterflow of superfluid helium (He II) plays a crucial role in understanding its heat transfer behavior and in designing effective flow channels to minimize experimental uncertainties. This study investigates the development process of He II counterflow in a two-dimensional channel through numerical simulations that couple the two-fluid model with Vinen's equation. Our findings identify three distinct flow regions and highlight the significant impact of mutual friction on flow development characteristics. The dimensionless development length exhibits a strong dependency on temperature and Reynolds number. A critical channel width for the superfluid component is observed below which the development length increases markedly. Notably, a Poiseuille velocity profile at the inlet necessitates a longer development length compared to uniform or “M”-shaped profiles, likely due to a more uneven distribution of mutual friction force near the inlet. These insights enhance our understanding of quantum fluid behavior and provide valuable guidance for experimental design in thermal counterflow studies.