Straight Vortex Research Articles

Helical vortices: linear stability analysis and nonlinear dynamics

We numerically investigate, within the context of helical symmetry, the dynamics of a regular array of two or three helical vortices with or without a straight central hub vortex. The Navier–Stokes equations are linearised to study the instabilities of such basic states. For vortices with low pitches, an unstable mode is extracted which corresponds to a displacement mode and growth rates are found to compare well with results valid for an infinite row of point vortices or an infinite alley of vortex rings. For larger pitches, the system is stable with respect to helically symmetric perturbations. In the nonlinear regime, we follow the time-evolution of the above basic states when initially perturbed by the dominant instability mode. For two vortices, sequences of overtaking events, leapfrogging and eventually merging are observed. The transition between such behaviours occurs at a critical ratio involving the core size and the vortex-separation distance. Cases with three helical vortices are also presented.

Determining the vortex tilt relative to a superconductor surface

It is of interest to determine the exit angle of a vortex from a superconductor surface, since this affects the intervortex interactions and their consequences. Two ways to determine this angle are to image the vortex magnetic fields above the surface, or the vortex core shape at the surface. In this work we evaluate the field $\mathbit{h}(x,y,z)$ above a flat superconducting surface $x,y$ and the currents $\mathbit{J}(x,y)$ at that surface for a straight vortex tilted relative to the normal to the surface, for both the isotropic and anisotropic cases. In principle, these results can be used to determine the vortex exit tilt angle from analyses of magnetic field imaging or density of states data.

Analytical Estimate of Rotor Blade Flapping Caused by a Straight Vortex Disturbance

Based on blade element/momentum theory the aerodynamic impact on rotor blade flapping caused by a straight line vortex lying in the plane of a rotor disk is solved analytically for the first time using a realistic swirl velocity profile. The consequences on rotor coning and cyclic flapping motion can thus be computed in closed-form. Results are given for a rotor subjected to a wake vortex of a large aircraft and for that of a large wind turbine.

Experimental and numerical study on the effect of the convergence angle, injection pressure and injection number on thermal performance of straight vortex tube

Experimental and numerical study on the effect of the convergence angle, injection pressure and injection number on thermal performance of straight vortex tube

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating trapped Bose-Einstein condensate, which is in the Thomas-Fermi regime at zero temperature and described by the Gross-Pitaevskii equation, is considered in the hydrodynamic "anelastic" approximation. In the presence of a smoothly inhomogeneous array of filaments (vortex lattice), a non-canonical Hamiltonian equation of motion is derived for the macroscopically averaged vorticity, with taking into account the spatial non-uniformity of the equilibrium condensate density determined by the trap potential. A minimum of the corresponding Hamiltonian describes a static configuration of deformed vortex lattice against a given density background. The minimum condition is reduced to a vector nonlinear partial differential equation of the second order, for which some approximate and exact solutions are found. It is shown that if the condensate density has an anisotropic Gaussian profile then equation of motion for the averaged vorticity admits solutions in the form of a spatially uniform vector with a nontrivial time dependence. An integral representation is obtained for the matrix Green function determining the non-local Hamiltonian of a system of arbitrary shaped vortex filaments in a condensate with Gaussian density. ... A simple approximate expression for the two-dimensional Green function is suggested at rather arbitrary density profile, and its successful comparison to the exact result in the Gaussian case is done. Approximate equations of motion are derived which describe a long-wave dynamics of interacting vortex filaments in condensates with the density depending on the transverse coordinates only.

Vortex dynamics in coherently coupled Bose-Einstein condensates

In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interaction with other vortices. Two such positive straight vortices experience a repulsive interaction and precess in a positive (anticlockwise) sense around their common centroid. A similar picture applies to vortices in a two-component two-dimensional uniform Bose-Einstein condensate (BEC) coherently coupled through rf Rabi fields. Unlike the classical case, however, the rf Rabi coupling induces an attractive interaction and two such vortices with positive signs now rotate in the negative (clockwise) sense. Pairs of counter-rotating vortices are instead found to translate with uniform velocity perpendicular to the line joining their cores. This picture is extended to a single vortex in a two-component trapped BEC. Although two uniform vortex-free components experience familiar Rabi oscillations of particle-number difference, such behavior is absent for a vortex in one component because of the nonuniform vortex phase. Instead the coherent Rabi coupling induces a periodic vorticity transfer between the two components.

Computation of Hydrodynamic Characteristics of A Marine Propeller Using Induction Factor Method Based on Normal Induced Velocity

In this study, induced velocity is determined with accuracy by overcoming the assumption of the vortex theory in calculating the induced velocity. The characteristics of a two bladed propeller are determined based on this velocity. The dominant parameters for the determination of the propeller characteristics are blade pitch angle, chord/diameter ratio, value of advance coefficient, position of blade sections and number of blades. The induction factor,the ratio of nomal induced velocities for helical and straight vortex respectively,is calculated to determin the normal induced velocity and then other characteristics. By keeping the values of propeller pitch and diameter constant with the filament of trailing vortices which produce helical surfaces extending infinitely backwards,the characteristics of propeller like lift coefficient, drag coefficient, thrust coefficient, torque coefficient and efficiency are derived for various blade sections and the values are compared with other experimental results.

Analytical Estimate of Rotor Controls Required for a Straight Vortex Disturbance Rejection

Based on blade element/momentum theory the aerodynamic impact of a straight line vortex lying in the plane of a rotor disk is solved analytically for the first time using a realistic swirl velocity profile. The consequences on rotor thrust, on blade aerodynamic moment about the hub and on the collective and cyclic controls needed for disturbance rejection can thus be computed in closed-form. Results are given for a rotor subjected to a wake vortex of a large wind energy turbine.

Leapfrogging Kelvin waves

Two vortex rings can form a localized configuration whereby they continually pass through one another in an alternating fashion. This phenomenon is called leapfrogging. Using parameters suitable for superfluid helium-4, we describe a recurrence phenomenon that is similar to leapfrogging, which occurs for two coaxial straight vortex filaments with the same Kelvin wave mode. For small-amplitude Kelvin waves we demonstrate that our full Biot-Savart simulations closely follow predictions obtained from a simpified model that provides an analytical approximation developed for nearly parallel vortices. Our results are also relevant to thin-cored helical vortices in classical fluids.

Direct numerical simulation of a straight vortex tube in a laminar boundary-layer flow

Direct numerical simulation of a straight vortex tube in a laminar boundary-layer flow

Simulation Methods for Aircraft Encounters with Deformed Wake Vortices

Simulation of aircraft wake-vortex encounters is regularly applied in the research toward revised aircraft separation minima. Most encounter flight simulation studies have used a pair of straight counter-rotating vortices. However, after being shed by the generating aircraft, the wake vortices begin to develop a growing deformation due to the long-wave Crow instability, especially under low-turbulent atmospheric conditions when vortices decay slowly. In this study, two methods for simulation of aircraft encounters with such perturbed wake vortices are described and compared. The first method uses a vortex simulation model, which is based on analytical models of the deformation that consider the large-scale vortex shapes. The second method applies vortex-velocity fields from high-fidelity large-eddy simulations. It offers the highest possible level of realism and is used as the reference. The resulting aircraft responses induced by wavy vortices and vortex rings are reproduced with good quality by the vortex simulation model. The comparison of both methods shows that the vortex simulation model captures the overall impact of vortex deformation on the aircraft upsets. It can be used for future safety assessments that require a large number of encounter simulations.

Axially symmetric equations for differential pulsar rotation with superfluid entrainment

In this article we present an analytical two-component model for pulsar rotational dynamics. Under the assumption of axial symmetry, implemented by a paraxial array of straight vortices that thread the entire neutron superfluid, we are able to project exactly the 3D hydrodynamical problem to a 1D cylindrical one. In the presence of density dependent entrainment the superfluid rotation is non-columnar: we circumvent this by using an auxiliary dynamical variable directly related to the areal density of vortices. The main result is a system of differential equations that take consistently into account the stratified spherical structure of the star, the dynamical effects of non-uniform entrainment, the differential rotation of the superfluid component and its coupling to the normal crust. These equations represent a mathematical framework in which to test quantitatively the macroscopic consequences of the presence of a stable vortex array, a working hypothesis widely used in glitch models. Even without solving the equations explicitly, we are able to draw some general quantitative conclusions; in particular, we show that the reservoir of angular momentum (corresponding to recent values of the pinning forces) is enough to reproduce the largest glitch observed in the Vela pulsar, provided its mass is not too large.

Hybrid artificial pinning centers of elongated-nanorods and segmented-nanorods in YBa2Cu3O7 films

To control the anisotropy of critical current density (Jc), hybrid artificial pinning centers (APCs) of elongated-nanorods and segmented-nanorods were incorporated into YBa2Cu3O7 films. The elongated-nanorods and segmented-nanorods were formed by fabricating multilayer films using YBa2Cu3O7+BaSnO3 targets with a different BaSnO3 content. According to the elastic calculation, the BaSnO3-free YBa2Cu3O7 regions between BaSnO3 segmented-nanorods were highly strained, resulting in their alignment along the c-axis. Pinning of the vortex kinks and straight vortices by the nanorod ends improved Jc in a wide range around B//ab. The angular dependence of Jc systematically varied with the multilayer structure of layer thickness and BSO content. Jc depended on the layer thickness even with keeping the constant average BSO content, showing that the BaSnO3 distribution, as well as the average BaSnO3 content, affected the Jc. The hybrid pinning effect of elongated-nanorods and nanorod ends improved the Jc anisotropy although the effect was not so large in the present films. The control of strain and interface is expected to lead to further improvement of Jc.

Simulation study of wake encounters with straight and deformed vortices

ABSTRACTA simulation study was conducted in order to investigate the influence of vortex deformation on wake encounter characteristics. Wake vortices tend to be strongly deformed during the decay process, depending on the atmospheric conditions in terms of turbulence and thermal stratification. For quantification of the influence of vortex deformation, encounters of an aircraft of the ‘Medium’ category behind a generator aircraft of the ‘Heavy’ category were simulated with straight vortices and with realistically deformed vortices derived from large-eddy simulations. All relevant parameters that influence the encounter characteristics, such as encounter angles and positions, were varied within a wide range. In order to cover all kinds of vortex deformation, encounters with different vortex ages from 16-136 seconds were simulated. Hence, all relevant phases during the vortex decay from nearly straight and wavy vortices to vortex rings were considered.The parameter variation study revealed that on average the impact on the encountering aircraft is less with deformed vortices than with straight vortices of comparable strength. Especially with vortex rings, the encountering aircraft is exposed to a much smaller impact. However, the results also show a larger aircraft response during encounters with wavy vortices just prior to vortex linking. The maximum aircraft response with wavy vortices is stronger than with straight vortices of comparable strength. Also, the strongest encounters occur under greater encounter angles with deformed vortices than with straight ones.

Application of Quasi-Continuous Method to Open-Water Characteristics Predictions of Propellers with Energy-Saving Ducts

The quasi-continous method (QCM) was applied to open-water thrust and torque predictions of ducted propellers with different positions of the propeller and duct. Two methods to calculate the resultant velocity were discussed. The QCM results are in good agreement with the experimental data of the propellers positioned inside a duct. The results of propellers in the downstream part of the duct show no significant dependence on the length of the straight trailing vortex of the duct. Comparison with the results calculated without any duct indicates no improvement of the open-water characteristics calculated by positioning the present duct in front of the present propeller.

Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation

In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26, 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self-similar solutions to the model and demonstrate that these types of solutions can model vortex kinks that gradually smooth and radiate Kelvin waves as time increases. Such solutions qualitatively agree with what one might expect from post-reconnection events.

Superconducting magnetoresistance effect observed in Co/Nb/Co trilayers under a parallel magnetic field: The importance of matching the width of magnetic domain walls of the Co layers with the thickness of the Nb interlayer

Magnetoresistance effects observed in ferromagnet/superconductor (FM/SC) hybrids, FM/SC bilayers (BLs) and FM/SC/FM trilayers (TLs), have attracted much interest. Here, we focus on the stray-fields-based superconducting magnetoresistance effect (sMRE) observed in Co(dCo)/Nb(dNb)/Co(dCo) TLs with sufficiently thick Co outer layers so that out-of-plane magnetic domains (MDs) and MDs walls (MDWs) emerge all over their surface when subjected to a parallel external magnetic field, Hex, equal to the coercive field, Hc. To explore the conditions necessary for maximization of the sMRE, we focus on the different kinds of the stray dipolar fields, Hdip, that emerge at the interior of the out-of-plane MDs and at the boundaries of MDWs; these have a different inherent tendency to create straight and semi-loop vortices, respectively. In the recent literature, the creation of straight and semi-loop vortices has been addressed at some extent both theoretically [Laiho et al., Phys. Rev. B 67, 144522 (2003)] and experimentally [Bobba et al., Phys. Rev. B 89, 214502 (2014)] for the case of FM/SC BLs. Here, we address these issues in FM/SC/FM TLs in connection to the sMRE. Specifically, we focus on an experimental finding reported recently [D. Stamopoulos and E. Aristomenopoulou, J. Appl. Phys. 116, 233908 (2014)]; strong magnetostatic coupling of the FM outer layers is accompanied by an intense sMRE in TLs in which the thickness of the SC interlayer, dSC, matches the width of MDWs, DMDWs. To investigate this finding, we employ simulations-modeling and energy-considerations and propose two quantitative criteria that facilitate the creation of straight vortices over semi-loop ones. The first focuses on the maximization of the stray Hdip that occur at the interior of the out-of-plane MDs. The second enables the estimation of a crossover between the preferable creation of one kind of vortices over the other. Both criteria respond well, when tested against experimental results. These generic criteria on the interference between dSC and DMDWs can assist the design of cryogenic devices based on FM/SC/FM TLs.

A differentiated plane wave as an electromagnetic vortex

Differentiating a complex scalar plane wave with respect to its direction produces an isolated straight vortex line and has a natural extension, described in earlier papers, to the vector waves of electromagnetism—a differentiated plane wave (DPW). It epitomizes destructive interference and will be shown to have the local structure of an electromagnetic vortex. In this paper its polarization structure and Poynting vector field are compared and contrasted with that of the family of linear polynomial waves, of which it is a special member. By definition this wider family has a general linear complex vector function of position multiplying a plane wave, but the function must be such that the combination satisfies Maxwell’s equations. This forces translational invariance of the function along the wavevector direction—in other words the wave is ‘non-diffracting’. In a natural sense all possible polarizations are exhibited once only. But the DPW has a distinctive polarization structure only partly explored previously. Both classes of waves share similar Poynting vector fields, which can be ‘elliptic’ (helix-like flow lines) or ‘hyperbolic’, of a repulsive nature, unexpected for a vortex. Both classes can be considered as a limit in the superposition of three closely parallel ordinary plane waves in destructive interference, and this derivation is supplied in full here.

On the absence of asymmetric wakes for periodically plunging finite wings

It has previously been shown that, at high Strouhal numbers, oscillating airfoils can produce deflected jets that can create very high lift-coefficients for otherwise symmetric scenarios. These deflected jets form through pairing of the trailing-edge vortices to create asymmetric vortex couples that self-propel at an angle to the freestream, resulting in an asymmetric flow field and non-zero lift. In this paper results are presented that indicate these high-lift deflected jets cannot form for finite wings. Instead of the straight vortex tubes that pair and convect at an angle to the freestream observed for effectively infinite wings, finite wings exhibit vortex tubes that break into two branches near the tip forming double helix structures. One branch connects with the last vortex; one branch connects with the next vortex. This creates a long “daisy chain” of interconnected trailing edge vortices forming a long series of vortex loops. These symmetric flow fields are shown to persist for finite wings even to Strouhal numbers more than twice those required to produce asymmetric wakes on plunging airfoils. Two contributing reasons are discussed for why deflected jets are not observed. First the tip vortex creates three-dimensionality that discourages vortex coupling. Second, the symmetry of the circulation of the interconnected vortex loops, which has been confirmed by the experiments, is a natural consequence of the vortex topology. Therefore, the asymmetry in trailing edge vortex strength previously observed as characteristic of deflected jets cannot be supported for finite wings.

Quantum Monte Carlo study of a vortex in superfluidHe4and search for a vortex state in the solid

We have performed a microscopic study of a straight quantized vortex line in three dimensions in condensed $^{4}\mathrm{He}$ at zero temperature using the shadow path integral ground state method and the fixed phase approximation. We have characterized the energy and the local density profile around the vortex axis in superfluid $^{4}\mathrm{He}$ at several densities, ranging from below the equilibrium density up to the overpressurized regime. For the Onsager-Feynman (OF) phase our results are exact and represent a benchmark for other theories. The inclusion of backflow correlations in the phase improves the description of the vortex with respect to the OF phase by a large reduction of the core energy of the topological excitation. At all densities the phase with backflow induces a partial filling of the vortex core and this filling slightly increases with density. The core size slightly decreases for increasing density and the density profile has well defined density dependent oscillations whose wave vector is closer to the wave vector of the main peak in the static density response function rather than to the roton wave vector. Our results can be applied to vortex rings of large radius $R$ and we find good agreement with the experimental value of the energy as a function of $R$ without any free parameter. We have studied also $^{4}\mathrm{He}$ above the melting density in the solid phase using the same functional form for the phase as in the liquid. We found that off-diagonal properties of the solid are not qualitatively affected by the velocity field induced by the vortex phase, both with and without backflow correlations. Therefore we find evidence that a perfect $^{4}\mathrm{He}$ crystal is not a marginally stable quantum solid in which rotation would be able to induce off-diagonal long-range coherence.