Superfluid helium-4 hydrodynamics with discrete topological defects

In superfluid helium-4, a model of normal-fluid hydrodynamics and their coupling with topological defects (quantized vortices) of the order parameter (superfluid) is formulated. The model requires only material properties as input and applies to both laminar and turbulent flows, to both dilute and dense superfluid vortex tangles. By solving the model for the case of a normal-fluid vorticity Hopf link interacting with systems of quantized vortices, two vortex dynamical mechanisms of energy transfer from the normal fluid to the superfluid are indicated: (a) small superfluid rings expand to the size of the normal-fluid vortex link tubes and (b) superfluid rings with diameters similar to the diameters of the normal-fluid tubes succumb to axial-flow instabilities that excite small-amplitude wiggles which subsequently evolve into spiral waves along the superfluid vortex contours. The normal-fluid vorticity scale determines the upper size of the generated superfluid vorticity structures. A key role in energy transfer processes is played by an axial-flow instability of a superfluid vortex due to mutual-friction excitation by the normal fluid, which mirrors the instability of normal-fluid tubes due to mutual-friction excitation by the superfluid. Although the sites of superfluid vorticity generation are always in the neighborhood of intense normal-fluid vorticity events, the superfluid vortices do not mimic the normal-fluid vorticity structure and perform different motions. These vortex dynamical processes provide explanations for the phenomenology of fully developed finite temperature superfluid turbulence.