Vortex pinning by surface geometry in superfluid helium

Abstract

We present measurements of how a single vortex line in superfluid helium interacts with a macroscopic bump on the chamber wall. At a general level our measurements confirm computational work on vortex pinning by a hemispherical bump, but not all the details agree. Rather than observing a unique pin location, we find that a given applied velocity field can support pinning at multiple sites along the bump, both near its apex and near its edge. We also find that pinning is less favorable than expected. A vortex can pass near or even traverse the bump itself with or without pinning, depending on its path of approach to the bump.Vortex methods have appeared for decades in computational work on classical fluids in both two and three dimensions [1,2]. They track the vorticity, which is the curl of the velocity field, rather than the velocity itself. The velocity can then be extracted using the Biot-Savart law. Vortex methods apply naturally to situations where the vorticity is concentrated in particular regions of the fluid; applications range from simulating trailing vortices of aircraft [1] to doing time updates of the computer graphics in video games [3]. A main benefit is that evaluating the velocity field does not require tracking a fine grid of points.A complication for vortex methods is the treatment of the vortex cores, which in classical fluids change shape and size as vortex lines bend and move. Using a fixed size for the vortex cores, while more straightforward in conception and implementation, is valid only when the core size is small compared to all other length scales, including the local radius of curvature of the vortex and the spacing between the computational points along the vortex [4]. This restriction does apply naturally in superfluid 4 He, where the experimentally measured core radius is about 1.3Å, small enough to be ignored on typical computational and experimental length scales. Conveniently, direct comparison between superfluid hydrodynamics calculations and experiment becomes possible. In several cases such simulations accurately describe non-trivial experimental behaviors [5,6].Here we compare vortex pinning in experiment and calculation, finding discrepancies that may indicate a need to modify the computational treatment of surfaces. Our measurements track a single vortex in superfluid helium interacting with a macroscopic bump. We compare to the computational work of Schwarz [7], for a hemispherical bump on an otherwise flat wall. Schwarz uses a flow field that far from the bump is uniform and parallel to the wall. He finds that if the vortex is swept into the vicinity of the bump, the bump can capture and pin the vortex [7]. If the flow velocity is large the vortex continues to move, but for sufficiently low velocities it remains at the bump. The calculation uses no explicit pinning forces; rather, the stationary configuration comes about entirely from the vortex settling into an arrangement where the net velocity vanishes along its core. For a given flow velocity, the pinned vortex term...

Modelling turbulent flow of superfluid 4He past a rough solid wall in the T = 0 limit

“…Early evidence of quantized vorticity sticking to rough surfaces was observed in 1958 by Hall and Shoenberg in torsional-oscillator experiments [3]. Further studies involving rotating quantum turbulence [4], thermal counterflow [5] and vortex capture probes such as wires [6] and MEMS devices [7] aid in providing confirmation of the influence of surface roughness and vortex pinning on superfluid flows. Numerical studies have examined vortex motion in the presence of solid boundaries through use of the vortex filament model (VFM) [8][9][10][11][12][13][14][15][16] and the Gross-Pitaevskii model [17].…”