Inside Vortex Research Articles

Band-resolved Caroli-de Gennes-Matricon states of multiple-flux-quanta vortices in a multiband superconductor.

Superconductors are of type I or II depending on whether they form an Abrikosov vortex lattice. Although bulk lead (Pb) is classified as a prototypical type-I superconductor, we show that its two-band superconductivity allows for single-flux-quantum and multiple-flux-quanta vortices in the intermediate state at millikelvin temperature. Using scanning tunneling microscopy, the winding number of individual vortices is determined from the real space wave function of its Caroli-de Gennes-Matricon bound states. This generalizes the topological index theorem put forward by Volovik for isotropic electronic states to realistic electronic structures. In addition, the bound states due to the two superconducting bands of Pb can be separately detected and the two gaps close independently inside vortices. This yields strong evidence for a low interband coupling.

Playing pool on the beta-plane: how weak initial perturbations predetermine the long-term evolution of coherent vortices

Abstract

Topological orders competing for the Dirac surface state in FeSeTe surfaces

FeSeTe has recently emerged as a leading candidate material for the two-dimensional topological superconductivity (TSC). Two reasons for the excitement are the high $T_c$ of the system and the fact that the Majorana zero modes (MZMs) inside the vortex cores live on the exposed surface rather than at the interface of a heterostructure as in the proximitized topological insulators. However, the recent scanning tunneling spectroscopy data have shown that, contrary to the theoretical expectation, the MZM does not exist inside every vortex core. Hence there are ``full'' vortices with MZMs and ``empty'' vortices without MZMs. Moreover the fraction of ``empty'' vortices increase with an increase in the magnetic field. We propose the possibility of two distinct gapped states competing for the topological surface states in FeSeTe: the TSC and half quantum anomalous Hall (hQAH). The latter is promoted by magnetic field through the alignment of magnetic impurities such as Fe interstitials. When hQAH takes over the topological surface state, the surface will become transparent to scanning tunneling microscopy and the nature of the vortex in such region will appear identical to what is expected of the vortices in the bulk, i.e., empty. Unmistakable signature of the proposed mechanism for empty vortices will be the existance of chiral Majorana modes(CMM) at the domain wall between a hQAH region and a TSC region. Such CMM should be observable by observing local density of states along a line connecting an empty vortex to a nearby full vortex.

Interaction between dual spherical particles during settling in fluid

Settling of solid particles in the fluid is one of the most basic forms of sediment transport. However, due to the complex particle–particle and particle–fluid interactions, the mechanism of settling is not yet fully understood. This study focuses on characterizing the dynamics of dual particles settling side by side. Both settling experiments and simulations are conducted with different initial spacings between particles and Reynolds numbers (Re). The range of Re is from 30 to 300, which corresponds to the transition zone between the Stokes and the Newton regime. Particle tracking velocimetry and particle image velocimetry are used in the experiments to determine particles’ trajectories and velocity fields around particles. A new electromagnetic release device is manufactured, which ensures accurate control of the initial condition. Together with the experiments, settling processes of particles are simulated based on discrete element–lattice Boltzmann method to investigate detailed flow structures. The results show that no attraction exists between particles when released simultaneously side by side. The repulsion between the two particles is a result of the asymmetry between the inside and outside vortices, and this repulsion will vanish when the initial spacing exceeds 5 particle diameters. Depending on the repulsion between particles, the settling process can be divided into three stages. The results also demonstrate that the initial spacing of the particles and Re are the two key parameters in the determination of the final settling velocity and separation distance. Their influence can be separated into two phase regimes depending on a critical Re (≈60), which is consistent with the one for the appearance of the Karman vortex street. In regime I (Re < 60), the settling process is dominated by viscous effects, and the effect of vortex interaction starts to take dominance in regime II (Re > 60). Overall, small initial spacing and large Re lead to strong repulsion between particles.

Numerical investigation of partial cavitation regimes over a wedge using large eddy simulation

Partial cavitation over incipient, transitory and periodic regimes is investigated using large eddy simulation (LES) in the (experimental) sharp wedge configuration of Ganesh et al. (2016). The numerical approach is based on a compressible homogeneous mixture model with finite rate mass transfer between the phases. Physical mechanisms of cavity transition observed in the experiments; i.e. re-entrant jet and bubbly shock wave, are both captured in the LES over their respective regimes. Vapor volume fraction data obtained from the LES is quantitatively compared to X-ray densitometry. In the transitory and periodic regimes, void fractions resulting from complex interactions of large regions of vapor in the sheet/cloud show very good comparison with the experiments. In addition, very good agreement with the experiments is obtained for the shedding frequency and the bubbly shock wave propagation speed. In the incipient regime, the qualitative characteristics of the flow (e.g. cavitation inside spanwise vortices in the shear layer) are captured in the simulations. Conditions favoring either the formation of the re-entrant jet or the bubbly shock wave are analyzed by contrasting the LES results between the regimes. In the transitory regime, large pressure recovery from within the cavity to outside, and the resulting high adverse pressure gradient at the cavity closure support the formation of re-entrant jet. In the periodic regime, overall low pressures lead to reduced speed of sound and increased medium compressibility, favoring the propagation of shock waves. In a re-entrant jet cycle, vapor production occurs predominantly in the shear layer, and intermittently within the cavity. In a bubbly shock cycle, vapor production is observed spanning the entire thickness of the cavity. Bubbly shock wave propagation is observed to be initiated by the impingement of the collapse-induced pressure waves from the previously shed cloud. Supersonic Mach numbers are observed in the cavity closure regions, while the regions within the grown cavity are subsonic due to the negligible flow velocities.

Shadowgraph Visualization of Turbulent Exchange between a Vortex Ring and the Environment at Different Densities of the Fluid in the Vortex Interior and Exterior

The turbulent exchange between a vortex ring and the environment was observed using shadowgraph imaging of the process when the density of the fluid inside and outside of the vortex is different. The characteristic distance of turbulent exchange traversed by the vortex is determined, and the dependence of this distance on the vortex velocity and the related Reynolds number is established.

Turbulence Appearance and Nonappearance in Thin Fluid Layers.

Flows in fluid layers are ubiquitous in industry, geophysics, and astrophysics. Large-scale flows in thin layers can be considered two dimensional with bottom friction added. Here we find that the properties of such flows depend dramatically on the way they are driven. We argue that a wall-driven (Couette) flow cannot sustain turbulence, no matter how small the viscosity and friction. Direct numerical simulations (DNSs) up to the Reynolds number Re=10^{6} confirm that all perturbations die in a plane Couette flow. On the contrary, for sufficiently small viscosity and friction, perturbations destroy the pressure-driven laminar (Poiseuille) flow. What appears instead is a traveling wave in the form of a jet slithering between wall vortices. For 5×10^{3}<Re<3×10^{4}, the mean flow in most cases has remarkably simple structure: the jet is sinusoidal with a parabolic velocity profile, and vorticity is constant inside vortices, while the fluctuations are small. At higher Re, strong fluctuations appear, yet the mean traveling wave survives. Considering the momentum flux barrier in such a flow, we derive a new scaling law for the Re dependence of the friction factor and confirm it by DNS.

Numerical analysis of flow and thermal patterns in a double-pipe Ranque-Hilsch vortex tube: Influence of cooling a hot-tube

Thermal efficiency and performance of a counter-flow vortex tube can be improved by cooling the main or hot-tube of the vortex tube. The present work investigates the effect of cooling (by water) a hot-tube on flow and thermal patterns (temperature separation) using a three-dimensional steady state model of turbulent swirling air flow inside vortex tube. The Computational Fluid Dynamics (CFD) was verified by comparing the present data with previous data reported in literature. In this work, the effects of performance parameters like length to diameter ratio (L/D) and number of nozzle intakes (N) on thermal separation of vortex tube within cooled hot-tube are also investigated numerically. The numerical data indicate that the cooling the hot-tube helps in increasing the cold air temperature difference, ΔTc, and improving isentropic efficiency of the system. The vortex tube with cooling water possesses higher cold air temperature differences and efficiencies than the one without cooling water by 6.3–10.3% and 5.8–10.6%, respectively. The highest temperature differences and efficiencies are belonging to the vortex tube with a cooled hot-tube at N = 4 and L/D = 47.5, and the lowest are belong to the vortex tube without a cooled hot-tube at N = 1 and L/D = 42.5.

A quantitative vortex-fluid description of Nernst effect in Bi-based cuprate high-temperature superconductors

We present a completely analytical vortex-fluid model describing several vortex-fluid phases of hole-doped cuprate superconductors below and above Tc. A key feature of the model is to synthesize several vortex damping mechanisms of scattering inside vortex core, core–core collisions and pinning. Accurate predictions for both magnetoresistance and Nernst effect are obtained, validated by measurements in six Bi-based cuprate samples over a wide range of temperature and magnetic fields, which strongly support the phase-fluctuation scenario in Bi-based cuprates. The model quantifies the unconventional vortex properties by a set of physical parameters, which adds quantitative contents to the discussions of pseudogap. A speculation is offered to use the vortex-fluid model as a first step towards achieving a comprehensive understanding of Nernst effect for all HTSC.

Numerical research of the compressible flow in a vortex tube using OpenFOAM software

The work presented in this paper is dealing with numerical simulation of energy separation mechanism and flow phenomena within a Ranque-Hilsch vortex tube. Simulation of turbulent, compressible, highly swirling flow inside vortex tube is performed using RANS approach, with Favre averaged conservation equations. For turbulence closure, k-? and k-? shear-stress transport models are used. It is assumed that the mean flow is axisymmetric, so the 2-D computational domain is used. Computations were performed using open-source CFD software Open- FOAM. All compressible solvers available within OpenFOAM were tested, and it was found that most of the solvers cannot predict energy separation. Code of two chosen solvers, which proved as the most robust, is modified in terms of mean energy equation implementation. Newly created solvers predict physically accepted behavior in vortex tube, with good agreement with experimental results. Comparison between performances of solvers is also presented.

Stability of Baroclinic Vortices on the β Plane and Implications for Transport

AbstractThis paper explores stability of and transport by baroclinic vortices on the β plane using a two-layer, quasigeostrophic model. The study adapts a wave–mean flow formalism and examines interactions between the axisymmetric flow (“the vortex”) and residuals (“the waves”). Unlike baroclinically unstable vortices on the f plane, such vortices on the β plane can be also vulnerable to barotropic instability as revealed by the globally integrated energy balance analysis. The spatial structure of energy fluxes shows the energy leakage inside the vortex core when its breakdown occurs. Mixing by stable and unstable vortical flows is quantified through the computation of finite-time Lyapunov exponent (FTLE) maps. Depending on the strength of wave radiation, the upper-layer FTLE maps of stable vortices show either an annulus or volute ring of vigorous mixing inside the vortex interior. This ring region is disrupted when the vortex becomes unstable. Both stable and unstable vortices show the wavy patterns of FTLE in the near and far fields. Despite the fact that the initial vortex resides in the top layer only, significant FTLE patterns are observed in the deep layer at later times. Lagrangian analysis of the vortex-induced change of large-scale tracer gradient demonstrates significant effects of vortex instability in the top layer and the importance of the wavelike anomalies in the bottom layer.

Performance of turbulence and cavitation models in prediction of incipient and developed cavitation

The aim of this article is to assess the impact of turbulence and cavitation models on the prediction of diesel injector nozzle flow. Two nozzles are examined, an enlarged one, operating at incipient cavitation, and an industrial injector tip, operating at developed cavitation. The turbulence model employed includes the re-normalization group k–ε, realizable k–ε and k–ω shear stress transport Reynolds-averaged Navier–Stokes models; linear pressure–strain Reynolds stress model and the wall adapting local eddy viscosity large eddy simulation model. The results indicate that all Reynolds-averaged Navier–Stokes and the Reynolds stress turbulence models have failed to predict cavitation inception due to their limitation to resolve adequately the low pressure existing inside vortex cores, which is responsible for cavitation development in this particular flow configuration. Moreover, Reynolds-averaged Navier–Stokes models failed to predict unsteady cavitation phenomena in the industrial injector. However, the wall adapting local eddy viscosity large eddy simulation model was able to predict incipient and developed cavitation, while also capturing the shear layer instability, vortex shedding and cavitating vortex formation. Furthermore, the performance of two cavitation methodologies is discussed within the large eddy simulation framework. In particular, a barotropic model and a mixture model based on the asymptotic Rayleigh–Plesset equation of bubble dynamics have been tested. The results indicate that although the solved equations and phase change formulation are different in these models, the predicted cavitation and flow field were very similar at incipient cavitation conditions. At developed cavitation conditions, standard cavitation models may predict unrealistically high liquid tension, so modifications may be essential. It is also concluded that accurate turbulence representation is crucial for cavitation in nozzle flows.

Two-fluid numerical simulations of turbulence inside Kelvin-Helmholtz vortices: Intermittency and reconnecting current sheets

The turbulence developing inside Kelvin-Helmholtz vortices has been studied using a two-fluid numerical simulation. From an initial large-scale velocity shear, the nonlinear evolution of the instability leads to the formation of a region inside the initial vortex characterized by small-scale fluctuations and structures. The magnetic energy spectrum is compatible with a Kolmogorov-like power-law decay, followed by a steeper power-law below proton scales, in agreement with other studies. The magnetic field increments show non-Gaussian distributions with increasing tails going towards smaller scales, consistent with presence of intermittency. The strong magnetic field fluctuations populating the tails of the distributions have been identified as current sheets by using the Partial Variance of the Increments (PVI) method. The strongest current sheets (largest PVI) appear around proton scales and below. By selecting several of such current sheets, it has been found that most of them are consistent with ongoing magnetic reconnection. The detailed study of one reconnecting current sheet as crossed by a virtual spacecraft is also presented. Inflow and outflow regions have been identified and the reconnection rate has been estimated. The observation of reconnection rates higher than typical fast rate ∼0.1 suggests that reconnection in turbulent plasma can be faster than laminar reconnection. This study indicates that intermittency and reconnecting current sheets are important ingredients of turbulence within Kelvin-Helmholtz vortices and that reconnection can play an important role for energy dissipation therein.

Numerical Investigation of Flow Characteristics in Counter Flow Vortex Tube

Despite of simplicity in construction and operation, determination of nature of flow physics parameters inside vortex tube is highly difficult due to presence of highly swirling and turbulent flow inside very small dimensional domain of vortex tube. At this point of difficulty, the methodology of Computational Fluid Dynamics can significantly help the researchers. Present paper is intended to discuss the outcomes of CFD study carried out on counter flow vortex tube. Standard k-ɛ turbulence model has been used to replicate the turbulence inside vortex tube. This model is found to be very well capable of predicting flow features inside vortex tube. Results indicate that cold mass fraction is an important parameter affecting the temperature separation magnitude in vortex tube. Cooling power separation is also an important parameter to evaluate performance of counter flow vortex tube, instead of cold end temperature only. A recirculating secondary flow has also been identified near the inlet region of vortex tube, which is accompanied by backflow at cold end for smaller values of cold mass fraction. Results of present CFD study are in good agreement with experimental results.

Possible realization of a chiralp-wave paired state in a two-component system

There is much interest in the realization of systems with p-wave pairing in one dimension or chiral p-wave pairing in two dimensions, because these are believed to support Majorana modes at the ends or inside vortices. We consider a two component system of composite fermions and provide theoretical evidence that, under appropriate conditions, the screened interaction between the minority composite fermions is such as to produce an almost exact realization of p-wave paired state described by the so-called anti-Pfaffian wave function. This state is predicted to occur at filling $\nu=3/8$ or 13/8 in GaAs when the Zeeman energy is sufficiently small, and at $\nu=\pm 3/8$ or $\pm 13/8$ in single layer graphene when either the Zeeman or the valley splitting is sufficiently small.

PARTICLE CONCENTRATION AT PLANET-INDUCED GAP EDGES AND VORTICES. I. INVISCID THREE-DIMENSIONAL HYDRO DISKS

We perform a systematic study of the dynamics of dust particles in protoplanetary disks with embedded planets using global 2-D and 3-D inviscid hydrodynamic simulations. Lagrangian particles have been implemented into magnetohydrodynamic code Athena with cylindrical coordinates. We find two distinct outcomes depending on the mass of the embedded planet. In the presence of a low mass planet ($8 M_{\oplus}$), two narrow gaps start to open in the gas on each side of the planet where the density waves shock. These shallow gaps can dramatically affect particle drift speed and cause significant, roughly axisymmetric dust depletion. On the other hand, a more massive planet ($>0.1 M_{J}$) carves out a deeper gap with sharp edges, which are unstable to the vortex formation. Particles with a wide range of sizes ($0.02<\Omega t_{s}<20$) are trapped and settle to the midplane in the vortex, with the strongest concentration for particles with $\Omega t_{s}\sim 1$. The dust concentration is highly elongated in the $\phi$ direction, and can be as wide as 4 disk scale heights in the radial direction. Dust surface density inside the vortex can be increased by more than a factor of 10$^2$ in a very non-axisymmetric fashion. For very big particles ($\Omega t_{s}\gg 1$) we find strong eccentricity excitation, in particular around the planet and in the vicinity of the mean motion resonances, facilitating gap opening there. Our results imply that in weakly turbulent protoplanetary disk regions (e.g. the "dead zone") dust particles with a very wide range of sizes can be trapped at gap edges and inside vortices induced by planets with $M_{p}<M_{J}$, potentially accelerating planetesimal and planet formation there, and giving rise to distinctive features that can be probed by ALMA and EVLA.

An analysis of the observed low‐level structure of rapidly intensifying and mature hurricaneEarl(2010)

We examine dynamic and thermodynamic aspects of Atlantic hurricaneEarl(2010) during its intensification and mature phases over four days of intensive measurements. During this period,Earlunderwent an episode of rapid intensification, maturity, secondary eyewall replacement, re‐intensification and the early part of its decline. The observations are used to appraise elements of a new model for tropical‐cyclone intensification.The results affirm the conventional (vortex interior) and boundary‐layer spin‐up mechanisms that form dynamical elements of the azimuthally averaged view of the new intensification model. The average maximum tangential winds beneath the eyewall are found to exceed the gradient wind by between 20 and 60%. The results suggest also that the gradient wind balance approximation in the low‐level vortex interior above the strong inflow layer may not be as accurate in the inner‐core region of a tropical cyclone during its intensification as has been widely held. An analysis of the low‐level thermodynamic structure affirms the radial increase of moist equivalent potential temperature,θe, with decreasing radius during the intensification process, a necessary ingredient of the new model for maintaining convective instability in the presence of a warming upper troposphere. An unanticipated finding is the discovery of an unmixed boundary layer in terms ofθewithin several hundred kilometres of the vortex centre. In the inner‐core region, this finding is not consistent with the axisymmetric eruption of the boundary layer into the eyewall unless there are non‐conservative (eddy) processes acting to modify the entropy of ascending air.

Laser-filament-induced snow formation in a subsaturated zone in a cloud chamber: Experimental and theoretical study

1 kHz, 2 mJ, 45 fs, 800 nm laser pulses were fired into a laboratory diffusion cloud chamber through a subsaturated zone (relative humidity ∼73%, T ∼ 4.3 °C). After 60 min of laser irradiation, an oval-shaped snow pile was observed right below the filament center and weighed ∼12.0 mg. The air current velocity at the edge of the vortices was estimated to be ∼16.5 cm/s. Scattering scenes recorded from the side show that filament-induced turbulence were formed inside the cloud chamber with two vortices below the filament. Two-dimensional simulations of the air flow motion in two cross sections of the cloud chamber confirm that the turbulent vortices exist below the filament. Based upon this simulation, we deduce that the vortices indeed have a three-dimensional elliptical shape. Hence, we propose that inside vortices where the humidity was supersaturated or saturated the condensation nuclei, namely, HNO(3), N(2)(+), O(2)(+) and other aerosols and impurities, were activated and grew in size. Large-sized particles would eventually be spun out along the fast moving direction towards the cold plate and formed an oval-shaped snow pile at the end.

A technique to identify vortex air using carbon monoxide observations

This study uses observations of carbon monoxide (CO) from the Microwave Limb Sounder instrument to identify vortex air in the winter polar regions. In particular, we use the probability distribution function (PDF) of the CO data to delineate CO concentrations characteristic of the interior of the vortex core as a function of space and time. This is achieved by fitting two Gaussian distributions to the PDF for a specific period and vertical level. These Gaussian fits are then examined to determine whether two chemically distinct regions exist by inspecting the intersection area between the Gaussians relative to their individual areas. When chemically distinct regions exist, the values of the fitted mean CO concentrations are representative of the interior and exterior of the polar vortex. To prove this point, a domain‐filling analysis is performed to produce high‐resolution maps. Comparison of these maps with the vortex edge derived using the equivalent latitude technique, and a statistical analysis over a range of years and isentropic levels, shows that the fitting scheme can be used to characterize measurements made inside the vortex during periods when chemically distinct populations exist. The statistical analysis also suggests that a threshold CO concentration can be derived based on the Gaussian fits which defines a good mixture between reducing the quantity of CO observations incorrectly identified as vortex interior air, whilst also minimizing the number of observations misclassified as vortex exterior air. This technique therefore provides an alternative to the dynamically derived calculation of values characteristic of the vortex interior.

Microwave spectroscopy of vortex dynamics in ortho-II YBa2Cu3O6.52

We present measurements of the vortex-state surface impedance, Z_s = R_s + i X_s, of a high quality, ortho-II-ordered single crystal of the cuprate high temperature superconductor YBa2Cu3O6.52 (T_c = 59K). Measurements have been made at four microwave frequencies (\omega/2\pi = 2.64, 4.51, 9.12 and 13.97 GHz), for magnetic fields ranging from 0 to 7 T. From these data we obtain the field, frequency and temperature dependence of the vortex viscosity, pinning constant, depinning frequency and flux-flow resistivity. The vortex viscosity, \eta(\omega,T), has a surprisingly strong frequency dependence and bears a striking resemblance to the zero-field quasiparticle conductivity, \sigma_qp(\omega,T), suggesting that the dominant dissipative mechanism for the flux lines is induced electric fields coupling to bulk, long-lived d-wave quasiparticles outside the vortex cores. This is in sharp contrast to the conventional Bardeen-Stephen picture, in which dissipation takes place inside quasi-normal vortex cores. The strong frequency dependence of the vortex viscosity in the microwave range requires us to treat it as a complex response function, with an imaginary part that is predicted to contribute to the apparent pinning force on the vortices. Measurements of the frequency dependence of the pinning force confirm that this term is present, and in a form consistent with the requirements of causality. At low temperatures the flux-flow resistivity, \rho_ff \propto 1/\eta, has the form \rho_ff(T) = \rho_0 + \rho_1 \ln(1/T), reminiscent of the DC resistivity of cuprates in the pseudogap regime.