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

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 for 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 dissipatio

Vortex solutions in a binary immiscible Bose-Einstein condensate

\ua9 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article\u27s title, journal citation, and DOI.We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices

Vortex-pair dynamics in three-dimensional homogeneous dipolar superfluids

The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices

Modelling Turbulent Flow of Superfluid ⁴He Past a Rough Solid Wall in the <em>T</em>= 0 Limit

\ua9 The Author(s) 2024.We present a numerical study, using the vortex filament model, of vortex tangles in a flow of pure superfluid 4He in the T=0 limit through a channel of width D=1 mm for various applied velocities V. The flat channel walls are assumed to be microscopically rough such that vortices terminating at the walls are permanently pinned; vortices are liberated from their pinned ends exclusively through self-reconnection with their images. Sustained tangles were observed, for a period of 80 s, above the critical velocity Vc∼0.20 cm s-1=20κD. The coarse-grained velocity profile was akin to a classical parabolic profile of the laminar Poiseuille flow, albeit with a nonzero slip velocity ∼ 0.20 cm s-1 at the walls. The friction force was found to be proportional to the applied velocity. The effective kinematic viscosity was ν′∼0.1κ, and effective Reynolds numbers within Re′&lt;200. The fraction of the polarised vortex length varied between zero in the middle of the channel and ∼ 60% within the shear flow regions ∼D/4 from the walls. Therefore, we studied a state of statically polarised ultraquantum (Vinen) turbulence fuelled at short length scales by vortex reconnections, including those with vortex images due to the relative motion between the vortex tangle and the pinning rough surface

Vortex Avalanches and Collective Motion in Neutron Stars

\ua9 2025. The Author(s). Published by the American Astronomical Society. We simulate the dynamics of about 600 quantum vortices in a spinning-down cylindrical container using a Gross-Pitaevskii model. For the first time, we find convincing spatial-temporal evidence of avalanching behavior resulting from vortex depinning and collective motion. During a typical avalanche, about 10-20 vortices exit the container in a short period, producing a glitch in the superfluid angular momentum and a localized void in the vorticity. After the glitch, vortices continue to depin and circulate around the vorticity void in a similar manner to that seen in previous point-vortex simulations. We present evidence of collective vortex motion throughout this avalanche process. We also show that the effective Magnus force can be used to predict when and where avalanches will occur. Finally, we comment on the challenge of extrapolating these results to conditions in real neutron stars, which contain many orders of magnitude more vortices

Reconnection dynamics and mutual friction in quantum turbulence

We investigate the behaviour of the mutual friction force in finite temperature quantum turbulence in 4He, paying particular attention to the role of quantized vortex reconnections. Through the use of the vortex filament model, we produce three experimentally relevant types of vortex tangles in steady-state conditions, and examine through statistical analysis, how local properties of the tangle influence the mutual friction force. Finally, by monitoring reconnection events, we present evidence to indicate that vortex reconnections are the dominant mechanism for producing areas of high curvature and velocity leading to regions of high mutual friction, particularly for homogeneous and isotropic vortex tangles

Cross-Component Energy Transfer in Superfluid Helium-4

\ua9 2024, Crown.The reciprocal energy and enstrophy transfers between normal fluid and superfluid components dictate the overall dynamics of superfluid 4He including the generation, evolution and coupling of coherent structures, the distribution of energy among lengthscales, and the decay of turbulence. To better understand the essential ingredients of this interaction, we employ a numerical two-way model which self-consistently accounts for the back-reaction of the superfluid vortex lines onto the normal fluid. Here we focus on a prototypical laminar (non-turbulent) vortex configuration which is simple enough to clearly relate the geometry of the vortex line to energy injection and dissipation to/from the normal fluid: a Kelvin wave excitation on two vortex anti-vortex pairs evolving in (a) an initially quiescent normal fluid, and (b) an imposed counterflow. In (a), the superfluid injects energy and vorticity in the normal fluid. In (b), the superfluid gains energy from the normal fluid via the Donnelly–Glaberson instability

Vortex Depinning in a Two-Dimensional Superfluid

\ua9 The Author(s) 2024.We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results

Drift velocity of bacterial chemotaxis in dynamic chemical environments

\ua9 2025 The Authors. Chemotaxis allows swimming bacteria to navigate through chemical landscapes. To date, continuum models of chemotactic populations (e.g. Patlak-Keller-Segel models) have considered bacteria responding only to spatial chemical gradients. In these models, chemotactic advection is modelled through a drift velocity proportional to the spatial chemical gradient. In nature and industry, however, bacterial populations experience dynamic, spatio-temporally varying chemical environments, such as the neighbourhood of lysing phytoplankton cells. Recent analyses have shown how temporal gradients can \u27confuse\u27 individual bacteria, impacting the precision of their gradient estimation. However, very few studies have considered how temporal gradients influence the chemotactic drift velocity of whole populations. Here, we use Monte Carlo simulations to infer the drift velocity of a population when both spatial and temporal gradients are present. We propose an ansatz for the drift velocity, which fits the simulations well. This ansatz allows us to account for how temporal gradients can significantly impact chemotaxis of bacterial populations up a spatial gradient. We explore the consequences of this new effect through a Patlak-Keller-Segel type model applied to single decaying and oscillating pulses of chemoattractant. Finally, we discuss possible biological consequences of our results and extensions of our modelling framework. This article is part of the theme issue \u27Biological fluid dynamics: emerging directions\u27