A note on the propagation of quantized vortex rings through a quantum turbulence tangle: Energy transport or dissipation?

We investigate the the role of vortex ring emission in the decay of quantum turbulence. Through geometric arguments and high resolution numerical simulations we study the effectiveness of vortex rings emission as a potential energy dissipation mechanism. We show the typical mean free path estimate for the distance a vortex ring propagates before reabsorption should be considered as a mean free path before reconnection. Furthermore, we provide evidence, supported by numerical simulations, to indicate that upon reconnection with a vortex line, a vortex ring will, on average, retain approximately $75\%$ of its energy. This leads to the much greater estimates for the distance energy can be transported by a vortex ring through a quantum turbulence tangle. Indeed, using typical experimental measurements, we conclude that a large proportion of the energy of the vortex ring will be dissipated at the boundaries. Ultimately, this provides evidence supporting the notion that vortex ring emission in quantum turbulence could be an effective energy dissipation mechanism, particularly for random unstructured tangle.