arXiv subjects

A. W. Baggaley

Publications and source records attributed to A. W. Baggaley.

At least 19 recordsLinked to original sources

arXiv2025

Out of Equilibrium Behaviour of Quantum Vortices: A Comparison of Point Vortex Dynamics and Fokker-Planck Evolution

An out of equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well-approximated by Fokker-Planck evolution only for very low initial energies per vortex, approximately less than -4, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent, $z$, in the dissipative point vortex model, undergoes a crossover, from a roughly constant value close to two for energy per vortex approximately greater than -4 to one which depends explicitly on the initial conditions for energy per vortex approximately less than -5.

cond-mat.quant-gas↗

arXiv2022

Vortex Solutions in a Binary Immiscible Bose-Einstein Condensate

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 quantised vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation to the two-component vortex solution for a range of atom numbers of the in-filling 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 in-filling component away from the centre of the vortex core, thereby demonstrating their stability to small perturbations.

cond-mat.quant-gas↗

arXiv2021

Mesoscale helicity distinguishes Vinen from Kolmogorov turbulence in helium II

Experiments and numerical simulations show that quantum turbulence exists in two distinct limiting regimes: Kolmogorov turbulence (which shares with classical turbulence the important property of a cascade of kinetic energy from large eddies to small eddies) and Vinen turbulence (which is more similar to a random flow). In this work, we define a mesoscale helicity for the superfluid, which, tested in numerical experiments, distinguishes the two turbulent regimes, quantifying the amount of nonlocal vortex interactions and the orientation of the vortex lines.

physics.flu-dyn↗

arXiv2020

Superfluid turbulence driven by cylindrically symmetric thermal counterflow

We show by direct numerical simulations that the turbulence generated by steadily heating a long cylinder immersed in helium~II is strongly inhomogeneous and consists of a dense turbulent layer of quantized vortices localized around the cylinder. We analyse the properties of this superfluid turbulence in terms of radial distribution of the vortex line density and the anisotropy and we compare these properties to the better known properties of homogeneous counterflow turbulence in channels.

physics.flu-dyn↗

arXiv2019

Knot spectrum of turbulence

Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the discrete (quantized) nature of vorticity can be exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose degree characterizes the topology of that vortex loop. By numerically simulating the dynamics of a tangle of quantum vortex lines, we find that this quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing and reforming, creating a distribution of topologies which we quantify in terms of a knot spectrum and its scaling law. We also find results analogous to those in the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the vortex length, as for macromolecules, and saturates above a characteristic length, as found for tumbled strings.

physics.flu-dyn↗

arXiv2018

Early warning signals in plant disease outbreaks

Summary 1. Infectious disease outbreaks in plants threaten ecosystems, agricultural crops and food trade. Currently, several fungal diseases are affecting forests worldwide, posing a major risk to tree species, habitats and consequently ecosystem decay. Prediction and control of disease spread are difficult, mainly due to the complexity of the interaction between individual components involved. 2. In this work, we introduce a lattice-based epidemic model coupled with a stochastic process that mimics, in a very simplified way, the interaction between the hosts and pathogen. We studied the disease spread by measuring the propagation velocity of the pathogen on the susceptible hosts. Quantitative results indicate the occurrence of a critical transition between two stable phases: local confinement and an extended epiphytotic outbreak that depends on the density of the susceptible individuals. 3. Quantitative predictions of epiphytotics are performed using the framework early-warning indicators for impending regime shifts, widely applied on dynamical systems. These signals forecast successfully the outcome of the critical shift between the two stable phases before the system enters the epiphytotic regime. 4. Synthesis: Our study demonstrates that early-warning indicators could be useful for the prediction of forest disease epidemics through mathematical and computational models suited to more specific pathogen-host-environmental interactions.

q-bio.PE↗

arXiv2018

Quantum ferrofluid turbulence

We study the elementary characteristics of turbulence in a quantum ferrofluid through the context of a dipolar Bose gas condensing from a highly non-equilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarized turbulence and density corrugations. The superfluid vortex lines and density fluctuations adopt a columnar or stratified configuration, depending on the sign of the dipolar interactions, with the vortices tending to form in the low density regions to minimize kinetic energy. When the interactions are dominantly dipolar, the decay of vortex line length is enhanced, closely following a $t^{-3/2}$ behaviour. This system poses exciting prospects for realizing stratified quantum turbulence and new levels of generating and controlling turbulence using magnetic fields.

cond-mat.quant-gas↗

arXiv2018

Kelvin-Helmholtz instability in an atomic superfluid

We demonstrate an experimentally feasible method for generating the classical Kelvin-Helmholtz instability in a single component atomic Bose-Einstein condensate. By progressively reducing a potential barrier between two counter-flowing channels we seed a line of quantised vortices, which precede to form progressively larger clusters, mimicking the classical roll-up behaviour of the Kelvin-Helmholtz instability. This cluster formation leads to an effective superfluid shear layer, formed through the collective motion of many quantised vortices. From this we demonstrate a straightforward method to measure the effective viscosity of a turbulent quantum fluid in a system with a moderate number of vortices, within the range of current experimental capabilities.

cond-mat.quant-gas↗

arXiv2017

Helicity and topology of a small region of quantum vorticity

We numerically study the evolution of a small turbulent region of quantised vorticity in superfluid helium, a regime which can be realised in the laboratory. We show that the turbulence achieves a fluctuating steady-state in terms of dynamics (energy), geometry (length, writhing) and topology (linking). After defining the knot spectrum, we show that, at any instant, the turbulence consists of many unknots and few large loops of great geometrical and topological complexity.

cond-mat.other↗

arXiv2016

Regimes of turbulence without an energy cascade

Experiments and numerical simulations of turbulent $^4$He and $^3$He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of quantum turbulent regimes without Kolmogorov scaling. This raises the important questions of why, in such regimes, the Kolmogorov spectrum fails to form, what is the physical nature of turbulence without energy cascade, and whether hydrodynamical models can account for the unusual behaviour of turbulent superfluid helium. In this work we describe simple physical mechanisms which prevent the formation of Kolmogorov scaling in the thermal counterflow, and analyze the conditions necessary for emergence of quasiclassical regime in quantum turbulence generated by injection of vortex rings at low temperatures. Our models justify the hydrodynamical description of quantum turbulence and shed light into an unexpected regime of vortex dynamics.

physics.flu-dyn↗

arXiv2015

Visualizing Pure Quantum Turbulence in Superfluid $^{3}$He: Andreev Reflection and its Spectral Properties

Superfluid $^3$He-B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in $^3$He-B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the inter-vortex separation.

cond-mat.other↗

arXiv2015

Local and nonlocal dynamics in superfluid turbulence

Turbulence in superfluid helium~II is a tangle of quantized vortex lines which interact via the classical Biot-Savart law. We show that vortex tangles with the same vortex line density will have different energy spectra, depending on the normal fluid which feeds energy into the superfluid component, and identify the spectral signature of two forms of superfluid turbulence: Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity field into local and nonlocal contributions, we find that in Vinen tangles the motion of vortex lines depends mainly on the local curvature, whereas in Kolmogorov tangles the long-range vortex interaction is dominant and leads to the formation of clustering of lines, in analogy to the 'worms` of ordinary turbulence.

cond-mat.other↗

arXiv2014

Coherent laminar and turbulent motion of toroidal vortex bundles

Motivated by experiments performed in superfluid helium, we study numerically the motion of toroidal bundles of vortex filaments in an inviscid fluid. We find that the evolution of these large-scale vortex structures involves the generalised leapfrogging of the constituent vortex rings. Despite three dimensional perturbations in the form of Kelvin waves and vortex reconnections, toroidal vortex bundles retain their coherence over a relatively large distance (compared to their size), in agreement with experimental observations.

physics.flu-dyn↗

arXiv2013

The Kelvin-wave cascade in the vortex filament model

The energy transfer mechanism in zero temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting Kelvin-waves to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with nonlocal six-wave Kelvin wave interactions as proposed by L'vov and Nazarenko.

cond-mat.other↗

arXiv2013

Vortex line density in counterflowing He II with laminar and turbulent normal fluid velocity profiles

Superfluid helium is an intimate mixture of a viscous normal fluid, with continuous vorticity, and an inviscid superfluid, where vorticity is constrained to thin, stable topological defects. One mechanism to generate turbulence in this system is through the application of a heat flux, so called thermal counterflow. Of particular interest is how turbulence in the superfluid responds to both a laminar and turbulent normal fluid in the presence of walls. We model superfluid vortex lines as reconnecting space curves with fixed circulation, and consider both laminar (Poiseuille) and turbulent normal fluid flows in a channel configuration. Using high resolution numerical simulations we show that turbulence in the normal fluid sustains a notably higher vortex line density than a laminar flow with the same mean flow rate. We exam Vinen's relation, $\sqrt{L}=γv_{ns}$, between the steady state vortex line density $L$ and the counterflow velocity $v_{ns}$. Our results support the hypothesis that transition to turbulence in the normal fluid is responsible for the TI to TII transition. We also consider the spectral properties of fluctuations of the superfluid vortices, which show a good agreement with previous experimental results.

physics.flu-dyn↗

arXiv2012

Quantum vortex reconnections

We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnection are time-symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium, and discuss the different length scales probed by the two models and by experiments.

cond-mat.other↗

arXiv2012

Thermally- and mechanically-driven quantum turbulence in helium II

Quantum turbulence can be generated in superfluid helium either thermally (by applying a heat flux, as in thermal counterflow) or mechanically (by stirring the liquid). By modelling the superfluid vortex lines as reconnecting space curves with fixed circulation, and the driving normal fluid as a uniform flow (for thermal counterflow) and a synthetic turbulent flow (for mechanically-driven turbulence), we determine the difference between thermally-driven and mechanically-driven quantum turbulence. We find that in mechanically-driven turbulence the energy is concentrated at the large scales, the spectrum obeys Kolmogorov scaling, vortex lines have large curvature, and the presence of coherent vortex structures induces vortex reconnections at small angles. On the contrary, in thermally-driven turbulence the energy is concentrated at the mesoscales, the curvature is smaller, the vorticity field is featureless and reconnections occur at larger angles. Our results suggest a method to experimentally infer the presence of superfluid vortex bundles.

cond-mat.other↗

arXiv2012

Cross-sections of Andreev scattering by quantized vortex rings in 3He-B

We studied numerically the Andreev scattering cross-sections of three-dimensional isolated quantized vortex rings in superfluid 3He-B at ultra-low temperatures. We calculated the dependence of the cross-section on the ring's size and on the angle between the beam of incident thermal quasiparticle excitations and the direction of the ring's motion. We also introduced, and investigated numerically, the cross-section averaged over all possible orientations of the vortex ring; such a cross-section may be particularly relevant for the analysis of experimental data. We also analyzed the role of screening effects for Andreev reflection of quasiparticles by systems of vortex rings. Using the results obtained for isolated rings we found that the screening factor for a system of unlinked rings depends strongly on the average radius of the vortex ring, and that the screening effects increase with decreasing the rings' size.

cond-mat.other↗