Three-dimensional vortex dynamics in superfluid ⁴He: Line-line and line-boundary interactions

The dynamical behavior of arbitrarily configured, interacting quantized vortex filaments is investigated by means of numerical experiments and analytical estimates. Several prototype situations of interest in the theory of superfluid turbulence and critical velocities are considered. It is shown that if a vortex loop approaches a surface to within a critical distance, a localized cusplike deformation is generated which drives the vortex into the surface at a well-defined point. If the vortex is reconnected to the surface in this limit, the two ends which now terminate on the surface quickly move apart. The entire process can be well approximated by making a simple reconnection at the critical distance. A similar process is found to occur when two vortex filaments try to cross, with two cusps developing which bring the lines together at a point in such a way that a line-line reconnection naturally ensues. More complicated versions of the reconnection process occur when a vortex terminates on a flat surface which contains a pinning site in the form of a local protrusion. Such a vortex is captured by the pinning site when it approaches to within a critical distance. Once a vortex is pinned, it requires a finite flow velocity to free it from the pinning site. At the depinning velocity, the vortex reconnects to the flat surface and moves off. An analytical depinning criterion involving both normal and superfluid velocities is derived, and found to be in good agreement with the numerical experiments.