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Author: Grafiati

Published: 11 March 2023

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1

Fonda, Enrico, Katepalli R. Sreenivasan, and Daniel P. Lathrop. "Reconnection scaling in quantum fluids." Proceedings of the National Academy of Sciences 116, no. 6 (January 22, 2019): 1924–28. http://dx.doi.org/10.1073/pnas.1816403116.

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Fundamental to classical and quantum vortices, superconductors, magnetic flux tubes, liquid crystals, cosmic strings, and DNA is the phenomenon of reconnection of line-like singularities. We visualize reconnection of quantum vortices in superfluid4He, using submicrometer frozen air tracers. Compared with previous work, the fluid was almost at rest, leading to fewer, straighter, and slower-moving vortices. For distances that are large compared with vortex diameter but small compared with those from other nonparticipating vortices and solid boundaries (called here the intermediate asymptotic region), we find a robust 1/2-power scaling of the intervortex separation with time and characterize the influence of the intervortex angle on the evolution of the recoiling vortices. The agreement of the experimental data with the analytical and numerical models suggests that the dynamics of reconnection of long straight vortices can be described by self-similar solutions of the local induction approximation or Biot–Savart equations. Reconnection dynamics for straight vortices in the intermediate asymptotic region are substantially different from those in a vortex tangle or on distances of the order of the vortex diameter.

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2

Lipniacki, Tomasz. "Evolution of quantum vortices following reconnection." European Journal of Mechanics - B/Fluids 19, no. 3 (May 2000): 361–78. http://dx.doi.org/10.1016/s0997-7546(00)00123-0.

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3

Enciso, Alberto, and Daniel Peralta-Salas. "Vortex reconnections in classical and quantum fluids." SeMA Journal 79, no. 1 (November 24, 2021): 127–37. http://dx.doi.org/10.1007/s40324-021-00277-8.

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AbstractWe review recent rigorous results on the phenomenon of vortex reconnection in classical and quantum fluids. In the context of the Navier–Stokes equations in $$\mathbb {T}^3$$ T 3 we show the existence of global smooth solutions that exhibit creation and destruction of vortex lines of arbitrarily complicated topologies. Concerning quantum fluids, we prove that for any initial and final configurations of quantum vortices, and any way of transforming one into the other, there is an initial condition whose associated solution to the Gross–Pitaevskii equation realizes this specific vortex reconnection scenario. Key to prove these results is an inverse localization principle for Beltrami fields and a global approximation theorem for the linear Schrödinger equation.

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4

Rorai, C., J. Skipper, R. M. Kerr, and K. R. Sreenivasan. "Approach and separation of quantised vortices with balanced cores." Journal of Fluid Mechanics 808 (November 4, 2016): 641–67. http://dx.doi.org/10.1017/jfm.2016.638.

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The scaling laws for the reconnection of isolated pairs of quantised vortices are characterised by numerically integrating the three-dimensional Gross–Pitaevskii equations, the simplest mean-field equations for a quantum fluid. The primary result is the identification of distinctly different temporal power laws for the pre- and post-reconnection separation distances $\unicode[STIX]{x1D6FF}(t)$ for two configurations. For the initially anti-parallel case, the scaling laws before and after the reconnection time $t_{r}$ obey the dimensional $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/2}$ prediction with temporal symmetry about $t_{r}$ and physical space symmetry about the mid-point between the vortices $x_{r}$. The extensions of the vortex lines close to reconnection form the edges of an equilateral pyramid. For all of the initially orthogonal cases, $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/3}$ before reconnection and $\unicode[STIX]{x1D6FF}\sim |t-t_{r}|^{2/3}$ after reconnection are respectively slower and faster than the dimensional prediction. For both configurations, smooth scaling laws are generated due to two innovations. The first innovation is to use an initial low-energy vortex-core density profile that suppresses unwanted density fluctuations as the vortices evolve in time. The other innovation is the accurate identification of the position of the vortex cores from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories allow us to calculate the Frenet–Serret frames and the curvature of the vortex lines, secondary results that might hold clues for the origin of the differences between the scaling laws of the two configurations. Reconnection takes place in a reconnection plane defined by the average tangents $\boldsymbol{T}_{av}$ and curvature normal $\boldsymbol{N}_{av}$ directions of the pseudo-vorticity curves at the points of closest approach, at time $t\approx t_{r}$. To characterise the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, from which four angles $\unicode[STIX]{x1D703}_{i}$ between the lines are defined. Their sum is convex or hyperbolic, that is $\sum _{i=1,4}\unicode[STIX]{x1D703}_{i}>360^{\circ }$, for the orthogonal cases, as opposed to the acute angles of the pyramid found for the anti-parallel initial conditions.

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5

Galantucci, Luca, Andrew W. Baggaley, Nick G. Parker, and Carlo F. Barenghi. "Crossover from interaction to driven regimes in quantum vortex reconnections." Proceedings of the National Academy of Sciences 116, no. 25 (June 6, 2019): 12204–11. http://dx.doi.org/10.1073/pnas.1818668116.

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Reconnections of coherent filamentary structures play a key role in the dynamics of fluids, redistributing energy and helicity among the length scales, triggering dissipative effects, and inducing fine-scale mixing. Unlike ordinary (classical) fluids where vorticity is a continuous field, in superfluid helium and in atomic Bose–Einstein condensates (BECs) vorticity takes the form of isolated quantized vortex lines, which are conceptually easier to study. New experimental techniques now allow visualization of individual vortex reconnections in helium and condensates. It has long being suspected that reconnections obey universal laws, particularly a universal scaling with time of the minimum distance between vortices δ. Here we perform a comprehensive analysis of this scaling across a range of scenarios relevant to superfluid helium and trapped condensates, combining our own numerical simulations with the previous results in the literature. We reveal that the scaling exhibits two distinct fundamental regimes: a δ∼t1/2 scaling arising from the mutual interaction of the reconnecting strands and a δ∼t scaling when extrinsic factors drive the individual vortices.

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6

Kimura, Y., and H. K. Moffatt. "Reconnection of skewed vortices." Journal of Fluid Mechanics 751 (June 20, 2014): 329–45. http://dx.doi.org/10.1017/jfm.2014.233.

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AbstractBased on experimental evidence that vortex reconnection commences with the approach of nearly antiparallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly antiparallel, they are annihilated on the strain time-scale, independent of kinematic viscosity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\nu $ in the limit $\nu \rightarrow 0$. When the vortices are skew to each other, they are annihilated under this action over a local extent that increases exponentially in the stretching direction, with clear evidence of reconnection on the same strain time-scale. The initial helicity associated with the skewed geometry is eliminated during the process of reconnection. The model applies equally to the reconnection of weak magnetic flux tubes under the action of a strain field, when Lorentz forces are negligible.

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7

Paoletti, M. S., Michael E. Fisher, and D. P. Lathrop. "Reconnection dynamics for quantized vortices." Physica D: Nonlinear Phenomena 239, no. 14 (July 2010): 1367–77. http://dx.doi.org/10.1016/j.physd.2009.03.006.

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8

Suaza Jaque, Ruben, and Oscar Velasco Fuentes. "Reconnection of orthogonal cylindrical vortices." European Journal of Mechanics - B/Fluids 62 (March 2017): 51–56. http://dx.doi.org/10.1016/j.euromechflu.2016.11.001.

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9

Andryushchenko, V. A., L. P. Kondaurova, and S. K. Nemirovskii. "Dynamics of Quantized Vortices Before Reconnection." Journal of Low Temperature Physics 185, no. 5-6 (April 13, 2016): 377–83. http://dx.doi.org/10.1007/s10909-016-1614-9.

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10

Califano, F., M. Faganello, F. Pegoraro, and F. Valentini. "Solar wind interaction with the Earth's magnetosphere: the role of reconnection in the presence of a large scale sheared flow." Nonlinear Processes in Geophysics 16, no. 1 (January 16, 2009): 1–10. http://dx.doi.org/10.5194/npg-16-1-2009.

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Abstract. The Earth's magnetosphere and solar wind environment is a laboratory of excellence for the study of the physics of collisionless magnetic reconnection. At low latitude magnetopause, magnetic reconnection develops as a secondary instability due to the stretching of magnetic field lines advected by large scale Kelvin-Helmholtz vortices. In particular, reconnection takes place in the sheared magnetic layer that forms between adjacent vortices during vortex pairing. The process generates magnetic islands with typical size of the order of the ion inertial length, much smaller than the MHD scale of the vortices and much larger than the electron inertial length. The process of reconnection and island formation sets up spontaneously, without any need for special boundary conditions or initial conditions, and independently of the initial in-plane magnetic field topology, whether homogeneous or sheared.

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11

Bavassano Cattaneo, M. B., M. F. Marcucci, Y. V. Bogdanova, H. Rème, I. Dandouras, L. M. Kistler, and E. Lucek. "Global reconnection topology as inferred from plasma observations inside Kelvin-Helmholtz vortices." Annales Geophysicae 28, no. 4 (April 1, 2010): 893–906. http://dx.doi.org/10.5194/angeo-28-893-2010.

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Abstract. During a long lasting period of northward interplanetary magnetic field and high solar wind speed (above 700 km/s), the Cluster spacecraft go across a number of very large rolled-up Kelvin-Helmholtz (KH) vortices at the dusk magnetopause, close to the terminator. The peculiarity of the present event is a particular sequence of ions and electrons distribution functions observed repeatedly inside each vortex. In particular, whenever Cluster crosses the current layer inside the vortices, multiple field-aligned ion populations appear, suggesting the occurrence of reconnection. In addition, the ion data display a clear velocity filter effect both at the leading and at the trailing edge of each vortex. This effect is not present in the simultaneous electron data. Unlike other KH studies reported in the literature in which reconnection occurs within the vortices, in the present event the observations are not compatible with local reconnection, but are accounted for by lobe reconnection occurring along an extended X-line at the terminator in the Southern Hemisphere. The reconnected field lines "sink" across the magnetopause and then convect tailward-duskward where they become embedded in the vortices. Another observational evidence is the detected presence of solar wind plasma on the magnetospheric side of the vortices, which confirms unambiguously the occurrence of mass transport across the magnetopause already reported in the literature. The proposed reconnection scenario accounts for all the observational aspects, regarding both the transport process and the kinetic signatures.

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12

Tsubota, Makoto, and Susumu Maekawa. "Reconnection of Quantized Vortices in Superfluid 4He." Journal of the Physical Society of Japan 61, no. 6 (June 1992): 2007–17. http://dx.doi.org/10.1143/jpsj.61.2007.

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13

Mansfield, P. "Quantum vortices." Nuclear Physics B 267, no. 3-4 (April 1986): 575–604. http://dx.doi.org/10.1016/0550-3213(86)90133-1.

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14

KUVSHINOV, B. N., V. P. LAKHIN, F. PEGORARO, and T. J. SCHEP. "Hamiltonian vortices and reconnection in a magnetized plasma." Journal of Plasma Physics 59, no. 4 (June 1998): 727–36. http://dx.doi.org/10.1017/s0022377898006655.

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Hamiltonian vortices and reconnection in magnetized plasmas are investigated analytically and numerically using a two-fluid model. The equations are written in the Lagrangian form of three fields that are advected with different velocities. This system can be considered as a generalization and extension of the two-dimensional Euler equation for an ordinary fluid. It is pointed out that these equations allow solutions in the form of singular current-vortex filaments, drift-Alfvén vortices and magnetic islands, and admit collisionless magnetic reconnection where magnetic flux is converted into electron momentum and ion vorticity.

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15

Mineev, V. P. "Half-quantum vortices." Low Temperature Physics 39, no. 10 (October 2013): 818–22. http://dx.doi.org/10.1063/1.4823487.

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16

van der Zant, H. S. J. "Quantum, ballistic vortices." Physica B: Condensed Matter 222, no. 4 (June 1996): 344–52. http://dx.doi.org/10.1016/0921-4526(96)00216-5.

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17

Nye, J. F. "Events in fields of optical vortices: rings and reconnection." Journal of Optics 18, no. 10 (August 31, 2016): 105602. http://dx.doi.org/10.1088/2040-8978/18/10/105602.

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18

Collado-Vega, Y. M., R. L. Kessel, D. G. Sibeck, V. L. Kalb, R. A. Boller, and L. Rastaetter. "Comparison between vortices created and evolving during fixed and dynamic solar wind conditions." Annales Geophysicae 31, no. 8 (August 30, 2013): 1463–83. http://dx.doi.org/10.5194/angeo-31-1463-2013.

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Abstract. We employ Magnetohydrodynamic (MHD) simulations to examine the creation and evolution of plasma vortices within the Earth's magnetosphere for steady solar wind plasma conditions. Very few vortices form during intervals of such solar wind conditions. Those that do remain in fixed positions for long periods (often hours) and exhibit rotation axes that point primarily in the x or y direction, parallel (or antiparallel) to the local magnetospheric magnetic field direction. Occasionally, the orientation of the axes rotates from the x direction to another direction. We compare our results with simulations previously done for unsteady solar wind conditions. By contrast, these vortices that form during intervals of varying solar wind conditions exhibit durations ranging from seconds (in the case of those with axes in the x or y direction) to minutes (in the case of those with axes in the z direction) and convect antisunward. The local-time dependent sense of rotation seen in these previously reported vortices suggests an interpretation in terms of the Kelvin–Helmholtz instability. For steady conditions, the biggest vortices developed on the dayside (about 6 RE in diameter), had their rotation axes aligned with the y direction and had the longest periods of duration. We attribute these vortices to the flows set up by reconnection on the high-latitude magnetopause during intervals of northward Interplanetary Magnetic Field (IMF) orientation. This is the first time that vortices due to high-latitude reconnection have been visualized. The model also successfully predicts the principal characteristics of previously reported plasma vortices within the magnetosphere, namely their dimension, flow velocities, and durations.

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19

Virk, D., F. Hussain, and R. M. Kerr. "Compressible vortex reconnection." Journal of Fluid Mechanics 304 (December 10, 1995): 47–86. http://dx.doi.org/10.1017/s0022112095004344.

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Reconnection of two antiparallel vortex tubes is studied as a prototypical coherent structure interaction to quantify compressibility effects in vorticity dynamics. Direct numerical simulations of the Navier-Stokes equations for a perfect gas are carried out with initially polytropically related pressure and density fields. For an initial Reynolds number (Re = Γ /v, circulation divided by the kinematic viscosity) of 1000, the pointwise initial maximum Mach number (M) is varied from 0.5 to 1.45. At M=0.5, not surprisingly, the dynamics are essentially incompressible. As M increases, the transfer of Γ starts earlier. For the highest M, we find that shocklet formation between the two vortex tubes enhances early Γ transfer due to viscous cross-diffusion as well as baroclinic vorticity generation. The reconnection at later times occurs primarily due to viscous cross-diffusion for all M. However, with increasing M, the higher early Γ transfer reduces the vortices’ curvature growth and hence the Γ transfer rate; i.e. for the Re case studied, the reconnection timescale increases with M. With increasing M, reduced vortex stretching by weaker ‘bridges’ decreases the peak vorticity at late times. Compressibility effects are significant in countering the stretching of the bridges even at late times. Our observations suggest significantly altered coherent structure dynamics in turbulent flows, when compressible.

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20

Corso, G., S. D. Prado, and S. Yoshida. "Quantum signature of reconnection bifurcations." Physica A: Statistical Mechanics and its Applications 295, no. 1-2 (June 2001): 316–20. http://dx.doi.org/10.1016/s0378-4371(01)00095-4.

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21

Liu, Z. X., and Y. D. Hu. "Local magnetic reconnection caused by vortices in the flow field." Geophysical Research Letters 15, no. 8 (August 1988): 752–55. http://dx.doi.org/10.1029/gl015i008p00752.

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22

Faganello, M., M. Sisti, F. Califano, and B. Lavraud. "Kelvin-Helmholtz instability and induced magnetic reconnection at the Earth’s magnetopause: a 3D simulation based on satellite data." Plasma Physics and Controlled Fusion 64, no. 4 (March 15, 2022): 044014. http://dx.doi.org/10.1088/1361-6587/ac43f0.

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Abstract A 3D two-fluid simulation, using plasma parameters as measured by MMS on 8 September 2015, shows the nonlinear development of the Kelvin–Helmholtz instability at the Earth’s magnetopause. It shows extremely rich dynamics, including the development of a complex magnetic topology, vortex merging and secondary instabilities. Vortex induced and mid-latitude magnetic reconnection coexist and produce an asymmetric distribution of magnetic reconnection events. Off-equator reconnection exhibits a predominance of events in the Southern Hemisphere during the early nonlinear phase, as observed by satellites at the dayside magnetopause. The late nonlinear phase shows the development of vortex pairing for all latitudes while secondary Kelvin–Helmholtz instability develops only in the Northern Hemisphere, leading to an enhancement of the occurrence of off-equator reconnection there. Since vortices move tailward while evolving, this suggests that reconnection events in the Northern Hemisphere should dominate at the nightside magnetopause.

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23

Kolář, Václav, and Jakub Šístek. "Vortex and the Balance between Vorticity and Strain Rate." International Journal of Aerospace Engineering 2019 (March 14, 2019): 1–8. http://dx.doi.org/10.1155/2019/1321480.

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A new analysis of the vortex-identification Q-criterion and its recent modifications is presented. In this unified framework based on different approaches to averaging of the cross-sectional balance between vorticity and strain rate in 3D, new relations among the existing modifications are derived. In addition, a new method based on spherical averaging is proposed. It is applicable to compressible flows, and it inherits a duality property which allows its use for identifying high strain-rate zones together with vortices. The new quantity is applied to identification of vortices and high strain-rate zones in the flow around an inclined flat plate, in the flow past a sphere, and for the reconnection process of two Burgers vortices.

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24

Hattori, Yuji. "Concentration of vorticity in a destabilized vortex due to selective decay." Journal of Fluid Mechanics 797 (May 24, 2016): 630–43. http://dx.doi.org/10.1017/jfm.2016.304.

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The formation of concentrated vortices like tornadoes and tropical cyclones in rotating fluids is of much interest in atmospheric flows. It is shown by direct numerical simulation that the selective decay of inviscid invariants leads to concentration of vorticity in a destabilized vortex. By selective decay we mean here that the circulation of the mean flow decays faster than the angular momentum or energy. Initially localized disturbances are superimposed onto the two-dimensional flattened Taylor–Green vortices to trigger the elliptic instability. In the later stage of nonlinear evolution of the disturbance circulation decays faster than angular momentum and energy, giving rise to a sharp peak in the vorticity distribution of the mean flow. During the selective decay vortex pairs reconnect and eventually annihilate at the cell boundaries of the Taylor–Green vortices. By evaluating the weight function of the inviscid invariants it is shown that the loss of angular momentum is much smaller than that of circulation when vorticity is lost at the cell boundary by reconnection or annihilation. Thus the reconnection and subsequent annihilation of vortex pairs is responsible for the selective decay and concentration of vorticity. The relevance of the mechanism to previous experiments and general cases is also discussed.

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25

Franci, Luca, Emanuele Papini, Alfredo Micera, Giovanni Lapenta, Petr Hellinger, Daniele Del Sarto, David Burgess, and Simone Landi. "Anisotropic Electron Heating in Turbulence-driven Magnetic Reconnection in the Near-Sun Solar Wind." Astrophysical Journal 936, no. 1 (August 26, 2022): 27. http://dx.doi.org/10.3847/1538-4357/ac7da6.

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Abstract We perform a high-resolution, 2D, fully kinetic numerical simulation of a turbulent plasma system with observation-driven conditions, in order to investigate the interplay between turbulence, magnetic reconnection, and particle heating from ion to subelectron scales in the near-Sun solar wind. We find that the power spectra of the turbulent plasma and electromagnetic fluctuations show multiple power-law intervals down to scales smaller than the electron gyroradius. Magnetic reconnection is observed to occur in correspondence of current sheets with a thickness of the order of the electron inertial length, which form and shrink owing to interacting ion-scale vortices. In some cases, both ion and electron outflows are observed (the classic reconnection scenario), while in others—typically for the shortest current sheets—only electron jets are present (“electron-only reconnection”). At the onset of reconnection, the electron temperature starts to increase and a strong parallel temperature anisotropy develops. This suggests that in strong turbulence electron-scale coherent structures may play a significant role for electron heating, as impulsive and localized phenomena such as magnetic reconnection can efficiently transfer energy from the electromagnetic fields to particles.

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26

Ben-Ya’acov, Uri. "Mechanism of quantum vortices’ intercommutation." Physical Review D 52, no. 2 (July 15, 1995): 1065–71. http://dx.doi.org/10.1103/physrevd.52.1065.

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27

Thompson, AM, and JMF Gunn. "Quantum dynamics of superfluid vortices." Physica C: Superconductivity 235-240 (December 1994): 2953–54. http://dx.doi.org/10.1016/0921-4534(94)91003-0.

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28

Ben-Ya'acov, Uri. "Unified dynamics of quantum vortices." Nuclear Physics B 382, no. 3 (September 1992): 597–615. http://dx.doi.org/10.1016/0550-3213(92)90661-t.

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29

Schliemann, J., and F. G. Mertens. "Vortices in quantum spin systems." European Physical Journal B 9, no. 2 (May 1999): 237–43. http://dx.doi.org/10.1007/s100510050762.

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30

Che, H., and G. P. Zank. "Electron Acceleration from Expanding Magnetic Vortices During Reconnection with a Guide Field." Astrophysical Journal 889, no. 1 (January 20, 2020): 11. http://dx.doi.org/10.3847/1538-4357/ab5d3b.

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31

Nykyri, K., and A. Otto. "Influence of the Hall term on KH instability and reconnection inside KH vortices." Annales Geophysicae 22, no. 3 (March 19, 2004): 935–49. http://dx.doi.org/10.5194/angeo-22-935-2004.

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Abstract. The Kelvin-Helmholtz instability (KHI) in its nonlinear stage can develop small-scale filamentary field and current structures at the flank boundaries of the magnetosphere. It has been shown previously with MHD simulations that magnetic reconnection can occur inside these narrow current layers, resulting in plasma transport from the solar wind into the magnetosphere. During periods of northward IMF, this transport is sufficient to generate a cold, dense plasma sheet on time scales consistent with satellite observations. However, when the length scales of these narrow current layers approach the ion inertia scale, the MHD approximation is not valid anymore and the Hall term in the Ohm's law must be included. We will study the influence of the Hall term on the KHI with 2-D Hall-MHD simulations and compare our results with corresponding MHD simulations. We estimate plasma transport velocities of the order of ~1.5km/s, thus confirming the results of the MHD approximation. However, the fine structure and the growth rates differ from the MHD approximation in an interesting way. Key words. Magnetospheric physics (magnetopause, cusp and boundary layers; plasma waves and instabilities), Space plasma physics (transport processes; magnetic reconnection; numerical simulation studies; nonlinear phenomena; turbulence)

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32

Haque, Q. "Electrostatic drift vortices in quantum magnetoplasmas." Physics of Plasmas 15, no. 9 (September 2008): 094502. http://dx.doi.org/10.1063/1.2982495.

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33

Haque, Q., and H. Saleem. "Ion acoustic vortices in quantum magnetoplasmas." Physics of Plasmas 15, no. 6 (June 2008): 064504. http://dx.doi.org/10.1063/1.2946434.

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34

Tong, David. "A quantum Hall fluid of vortices." Journal of High Energy Physics 2004, no. 02 (February 25, 2004): 046. http://dx.doi.org/10.1088/1126-6708/2004/02/046.

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35

Marchenko, V. I., and E. R. Podolyak. "On n-quantum vortices in superconductors." Journal of Experimental and Theoretical Physics 94, no. 1 (January 2002): 200–202. http://dx.doi.org/10.1134/1.1448622.

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36

Salomaa, M. M., and G. E. Volovik. "Half-Quantum Vortices in SuperfluidHe3-A." Physical Review Letters 55, no. 11 (September 9, 1985): 1184–87. http://dx.doi.org/10.1103/physrevlett.55.1184.

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37

Tejada, J., E. M. Chudnovsky, and A. García. "Quantum tunneling of vortices in theTl2CaBa2Cu2O8superconductor." Physical Review B 47, no. 17 (May 1, 1993): 11552–54. http://dx.doi.org/10.1103/physrevb.47.11552.

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38

Srivastava, Y. N., M. H. Friedman, and A. Widom. "Planer dynamics of charged quantum vortices." Lettere Al Nuovo Cimento Series 2 42, no. 5 (March 1985): 232–34. http://dx.doi.org/10.1007/bf02739461.

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39

Penna, Vittorio, and Mauro Spera. "A geometric approach to quantum vortices." Journal of Mathematical Physics 30, no. 12 (December 1989): 2778–84. http://dx.doi.org/10.1063/1.528512.

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40

Ben-Ya'acov, Uri. "Extended dual transformation including quantum vortices." Physics Letters B 274, no. 3-4 (January 1992): 352–56. http://dx.doi.org/10.1016/0370-2693(92)91997-n.

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41

Chou, Chia-Chun, and Robert E. Wyatt. "Quantum vortices within the complex quantum Hamilton–Jacobi formalism." Journal of Chemical Physics 128, no. 23 (June 21, 2008): 234106. http://dx.doi.org/10.1063/1.2937905.

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42

Treumann, R. A., W. Baumjohann, and W. D. Gonzalez. "Collisionless reconnection: magnetic field line interaction." Annales Geophysicae 30, no. 10 (October 9, 2012): 1515–28. http://dx.doi.org/10.5194/angeo-30-1515-2012.

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Abstract. Magnetic field lines are quantum objects carrying one quantum Φ0 = 2πh/e of magnetic flux and have finite radius λm. Here we argue that they possess a very specific dynamical interaction. Parallel field lines reject each other. When confined to a certain area they form two-dimensional lattices of hexagonal structure. We estimate the filling factor of such an area. Anti-parallel field lines, on the other hand, attract each other. We identify the physical mechanism as being due to the action of the gauge potential field, which we determine quantum mechanically for two parallel and two anti-parallel field lines. The distortion of the quantum electrodynamic vacuum causes a cloud of virtual pairs. We calculate the virtual pair production rate from quantum electrodynamics and estimate the virtual pair cloud density, pair current and Lorentz force density acting on the field lines via the pair cloud. These properties of field line dynamics become important in collisionless reconnection, consistently explaining why and how reconnection can spontaneously set on in the field-free centre of a current sheet below the electron-inertial scale.

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Chapelier, J. B., B. Wasistho, and C. Scalo. "Large-eddy simulation of temporally developing double helical vortices." Journal of Fluid Mechanics 863 (January 23, 2019): 79–113. http://dx.doi.org/10.1017/jfm.2018.910.

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This paper investigates the transient regime and turbulent wake characteristics of temporally developing double helical vortices via high-fidelity large-eddy simulation (LES) for circulation Reynolds numbers in the range $Re_{\unicode[STIX]{x1D6E4}}=7000{-}70\,000$, vortex-core radii between $r_{c}=0.06R$ and $0.2R$ and helical pitches in the range $h=0.36R{-}0.61R$, where $R$ is the initial helix radius. The present study achieves three objectives: (i) assess the influence of $Re_{\unicode[STIX]{x1D6E4}}$, $r_{c}$ and $h$ on the growth rates of the helical vortex instability driven by mutual inductance; (ii) characterize the type of vortex reconnection events that appear during transition; (iii) study the characteristics of turbulence in the far wake, and in particular quantify the anisotropy in the flow. The initial transient dynamics is conveniently described in terms of the non-dimensional time $t^{\star }=t\unicode[STIX]{x1D6E4}/h^{2}$, yielding the dimensionless growth rate of $\unicode[STIX]{x1D6FC}^{\ast }\sim 20$ and collapsing of all the LES data for a given $r_{c}/h$ ratio. The vortex-core displacement growth rate is found to be Reynolds-number independent, and decreases for larger $r_{c}/h$ ratios. Several vortex reconnection events are identified during the transition, mostly initiated by the leap frogging of helical vortices. This phenomenon causes the entanglement of orthogonal vortex filaments, leading to their separation, followed by the creation of elongated threads in the axial direction. The turbulent wake generated by the breakdown of the helical vortices is found to be highly anisotropic with the axial fluctuations being dominant compared to the radial and azimuthal fluctuations (near one-dimensional turbulence). The study of integral length scales shows the presence of a strong large-scale anisotropy, retaining the memory of the initial helical pitch $h$, in particular for the integral scale in the axial direction. The large-scale anisotropy is propagated through the inertial and dissipative ranges, determined from the computation of the moments of velocity gradients in the three directions.

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Howson, T. A., I. De Moortel, and D. I. Pontin. "Magnetic reconnection and the Kelvin-Helmholtz instability in the solar corona." Astronomy & Astrophysics 656 (December 2021): A112. http://dx.doi.org/10.1051/0004-6361/202141620.

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Context. The magnetic Kelvin-Helmholtz instability (KHI) has been proposed as a means of generating magnetohydrodynamic turbulence and encouraging wave energy dissipation in the solar corona, particularly within transversely oscillating loops. Aims. Our goal is to determine whether the KHI encourages magnetic reconnection in oscillating flux tubes in the solar corona. This will establish whether the instability enhances the dissipation rate of energy stored in the magnetic field. Methods. We conducted a series of three-dimensional magnetohydrodynamic simulations of the KHI excited by an oscillating velocity shear. We investigated the effects of numerical resolution, field line length, and background currents on the growth rate of the KHI and on the subsequent rate of magnetic reconnection. Results. The KHI is able to trigger magnetic reconnection in all cases, with the highest rates occurring during the initial growth phase. Reconnection is found to occur preferentially along the boundaries of Kelvin-Helmholtz vortices, where the shear in the velocity and magnetic fields is greatest. The estimated rate of reconnection is found to be lowest in simulations where the KHI growth rate is reduced. For example, this is the case for shorter field lines or due to shear in the background field. Conclusions. In non-ideal regimes, the onset of the instability causes the local reconnection of magnetic field lines and enhances the rate of coronal wave heating. However, we found that if the equilibrium magnetic field is sheared across the Kelvin-Helmholtz mixing layer, the instability does not significantly enhance the rate of reconnection of the background field, despite the free energy associated with the non-potential field.

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Vinen, W. F. "An introduction to quantum turbulence." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1877 (June 5, 2008): 2925–33. http://dx.doi.org/10.1098/rsta.2008.0084.

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This paper provides a brief introduction to quantum turbulence in simple superfluids, in which the required rotational motion in the superfluid component is due entirely to the topological defects that are identified as quantized vortices. Particular emphasis is placed on the basic dynamical behaviour of the quantized vortices and on turbulent decay mechanisms at a very low temperature. There are possible analogies with the behaviour of cosmic strings.

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Nykyri, K., and A. Otto. "Plasma transport at the magnetospheric boundary due to reconnection in Kelvin-Helmholtz vortices." Geophysical Research Letters 28, no. 18 (September 15, 2001): 3565–68. http://dx.doi.org/10.1029/2001gl013239.

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Nakamura, T. K. M., and M. Fujimoto. "Magnetic reconnection within MHD-scale Kelvin–Helmholtz vortices triggered by electron inertial effects." Advances in Space Research 37, no. 3 (January 2006): 522–26. http://dx.doi.org/10.1016/j.asr.2005.01.057.

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ZHANG, XIN-HUI, YI-SHI DUAN, YUXIAO LIU, and LI ZHAO. "SELF-DUAL VORTICES IN THE FRACTIONAL QUANTUM HALL SYSTEM." International Journal of Modern Physics B 24, no. 04 (February 10, 2010): 423–33. http://dx.doi.org/10.1142/s0217979209052480.

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Based on the ϕ-mapping theory, we obtain an exact Bogomol'nyi self-dual equation with a topological term, which is ignored in traditional self-dual equation, in the fractional quantum Hall system. It is revealed that there exist self-dual vortices in the system. We investigate the inner topological structure of the self-dual vortices and show that the topological charges of the vortices are quantized by Hopf indices and Brouwer degrees. Furthermore, we study the branch processes in detail. The vortices are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the vector field ϕ.

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Zhong, Z. H., M. Zhou, Yi-Hsin Liu, X. H. Deng, R. X. Tang, D. B. Graham, L. J. Song, H. Y. Man, Y. Pang, and Yu V. Khotyaintsev. "Stacked Electron Diffusion Regions and Electron Kelvin–Helmholtz Vortices within the Ion Diffusion Region of Collisionless Magnetic Reconnection." Astrophysical Journal Letters 926, no. 2 (February 1, 2022): L27. http://dx.doi.org/10.3847/2041-8213/ac4dee.

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Abstract The structure of the electron diffusion region (EDR) is essential for determining how fast the magnetic energy converts to plasma energy during magnetic reconnection. Conventional knowledge of the diffusion region assumes that the EDR is a single layer embedded within the ion diffusion region (IDR). This paper reports the first observation of two EDRs that stack in parallel within an IDR by the Magnetospheric Multiscale mission. The oblique tearing modes can result in these stacked EDRs. Intense electron flow shear in the vicinity of two EDRs induced electron Kelvin–Helmholtz vortices, which subsequently generated kinetic-scale magnetic peak and holes, which may effectively trap electrons. Our analyses show that both the oblique tearing instability and electron Kelvin–Helmholtz instability are important in three-dimensional reconnection since they can control the electron dynamics and structure of the diffusion region through cross-scale coupling.

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BEN-YA'ACOV, URI. "CORE STRUCTURE AND ENERGIES OF MULTIPLE-n QUANTUM VORTICES." International Journal of Modern Physics B 10, no. 22 (October 10, 1996): 2811–35. http://dx.doi.org/10.1142/s0217979296001276.

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Quantum vortices with a multiple winding number (n ≠ ±1) are interpretable as metastable states of | n | elementary vortices. The information on the structure of these metastable states is contained in the amplitude of the complex scalar field ϕ (x) which describes the medium in which the vortices appear. A direct measure of this structure is given by the core radius associated with the vortex that corresponds to the metastable state. Several algorithms are suggested for the calculation of the core radius of vortices, and other radii related to the vortex energy, from the knowledge of the amplitude | ϕ (x) |. These radii are numerically computed as functions of the winding number n of the vortices for nine different test models. All these sets are found to be linear in n to a very high accuracy in all the test models. Linear fits are calculated, with some parameters found to be model independent. General conclusions concerning the dependence of the vortex energy on the winding number are also obtained.

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