A Note on the Propagation of Quantized Vortex Rings Through a Quantum Turbulence Tangle: Energy Transport or Energy Dissipation?

Abstract

We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high resolution numerical simulations we examine the validity of simple estimates of the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately 75% of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipation.

Interactions between unidirectional quantized vortex rings

“…Our observation that small rings are created with high probability due to reconnections in the presence of strong deformations reinforces the view that the emission of small rings is likely to be a common feature in turbulent vortex tangles at low temperatures 21,25,28,30,32 . The time-dependent vortex line density L(t) during the free decay of uncorrelated tangles (created through vortex ring collisions) 17,37 in the zero-temperature limit was observed to be…”

“…2 as a function of b. We note that R ′ (b) for the smaller ring is qualitatively similar to that observed in recent simulations of the interaction between a vortex ring and an initially straight vortex line 32,47 . Further insight is provided by the amount of energy converted from translational motion of the ring into deformations.…”

“…less than half). The exact mechanism leading to the creation of these small rings is unknown although the production of small rings is a common feature in many theoretical and computational works on quantum turbulence near zero temperature [21][22][23][24][25][26][27][28][29][30][31][32] . Yet the question of whether the interaction between a pair of rings can produce rings of much smaller radii has not yet been addressed, and this paper seeks to shed further light on this issue by examining the efficiency for the creation of small rings when larger rings (both circular and deformed) interact with each other.…”

Regimes of turbulence without an energy cascade

“…This probability, which depends on the current vortex line density, L(t) and the size of experimental cell, D was investigated in detail in Ref. [30]. The probability p is close to unity when the tangle is still very dilute but decreases exponentially with both the vortex line density and the size of experimental cell.…”

Vortex simulations on a 3-sphere

“…Without the non-local term, the tangle can degenerate into an "open-orbit" state, consisting of straight parallel vortex lines that do not interact [7,8]. Keeping the non-local term solves this problem [9], but given the extra computational demands of the full integral even subsequent work has used LIA [30,31], compared results from LIA and the full integral [13,32], or drawn conclusions from prior LIA work [33]. Hence better understanding its limitations remains relevant.…”