Large Eddy Simulation of a Vortex Ring Impacting a Bump

A vortex ring impacting a three-dimensional bump is studied using large eddy simulation for a Reynolds number Re=$4$x$10^4$ based on the initial diameter and translational speed of the vortex ring. The effects of bump height and vortex core thickness for thin and thick vortex rings on the vortical flow phenomena and the underlying physical mechanisms are investigated. Based on the analysis of the evolution of vortical structures, two typical kinds of vortical structures, i.e., the wrapping vortices and the hair-pin vortices, are identified and play an important role in the flow state evolution. The boundary vorticity flux is analyzed to reveal the mechanism of the vorticity generation on the bump surface. The circulation of the primary vortex ring reasonably elucidates some typical phases of flow evolution. Further, the analysis of turbulent kinetic energy reveals the transition from laminar to turbulent state. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the flow evolution and the flow transition to turbulent state.     

Dynamics of a single vortex line in a Bose-Einstein condensate

We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 sec. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis.     

Experimental investigation of primary and secondary features in high-mach-number shock-bubble interaction

Experiments to study the compression and unstable evolution of an isolated soap-film bubble containing helium, subjected to a strong planar shock wave (M=2.95) in ambient nitrogen, have been performed in a vertical shock tube of square internal cross section using planar laser diagnostics. The early phase of the interaction process is dominated by the formation of a primary vortex ring due to the baroclinic source of vorticity deposited during the shock-bubble interaction, and the mass transfer from the body of the bubble to the vortex ring. The late time (long after shock interaction) study reveals the presence of a secondary baroclinic source of vorticity at high Mach number which is responsible for the formation of counterrotating secondary and tertiary vortex rings and the subsequent larger rate of elongation of the bubble.     

Effect of pressure evolution on the formation enhancement in dual interacting vortex rings

In the biological locomotion, the ambit pressure is of particular importance to use as a means of propulsion. The multiple vortex rings have been proved to generate additional thrust by interaction, but the mechanism of this thrust enhancement is still unknown. This study examines the effect of ambit pressure on formation enhancement in interacting dual vortex rings. The vortex rings, which have the same formation time, are successively generated in a piston-cylinder apparatus. The finite-time Lyapunov exponent (FTLE) visualizes the flow fields as an indication of Lagrangian coherent structures (LCSs), and the pressure field is calculated based on the digital particle image velocity (DPIV). We extract the back pressure of the rear vortex in dual vortices and the back pressure circulation $\varGamma_{\rm b}$, which is defined as a form of overpressure circulation $\varGamma_{\rm p}$. The $\varGamma_{\rm b}$ has a positive linear relationship with $\varGamma_{\rm p}$. A critical interval distance $d_{\rm cr}^*$ in a range of 0.32-0.42 is found where $\varGamma_{\rm b}$ and $\varGamma_{\rm p}$ reach the maximum synchronously, leading to a full-interaction mode. Moreover, an over-interaction mode and an under-interaction mode are proposed when the dimensionless interval distance $d^*$ is smaller or larger than $d_{\rm cr}^*$. To conclude, the high back pressure caused by vortex interaction can enhance the formation of vortex rings and lead to high thrust.     

Vortex chirality in exchange-biased elliptical magnetic rings

The flux-closed or "vortex" state in thin-film magnetic rings has been proposed as a data storage token, but it has proven difficult to control the vortex chirality in a simple manner. Here, a model is described that predicts the vortex chirality of an elliptical magnetic ring as a function of the direction of the applied field and of the exchange bias, based on the change in energy of the system as the domain walls move. Experimental measurements of chirality in Co and Co/IrMn magnetic rings with 3.2 microm major axis are in excellent agreement with the model. The vortex circulation direction can therefore be tailored with an appropriate combination of applied field direction and exchange bias direction with respect to the major axis.     

A coaxial vortex ring model for vortex breakdown

A simple-yet plausible-model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.     

Effects of notches on the order of flux-closure state formation in bi-rings by micromagnetic simulation

The effects of the number and the location of notches on the formation of flux-closure states in bi-rings with fields applied in the x direction (i.e., along the short axis direction of bi-rings) and y direction (i.e., along the long axis direction of bi-rings) are investigated using micromagnetic simulation. For the bi-rings with one notch and the bi-rings with two notches symmetric about y axis, the order of flux-closure state formation in each ring can be controlled. But the flux-closure state forms simultaneously in each ring for the bi-rings with two notches symmetric about x axis. For the bi-rings with two notches that are symmetric neither about x axis nor about y axis, only one ring can form a flux-closure state in the y-direction field and no flux-closure state can be found in rings in the x-direction field. Therefore, logic states can be defined by controlling the order of flux-closure state formation, which can be utilized in future logic devices.     

Propagation of orifice- and nozzle-generated vortex rings in air

The effect of the exit geometry of a vortex ring generator was studied experimentally. Two types of exit geometries were chosen: an orifice and a nozzle. Vortex rings were generated by pushing a solenoid-valve-controlled, pressurized-air jet through the circular opening of the orifice or nozzle. Experiments were performed over a wide range of initial Reynolds number (450≤Re≤4580) and length-to-diameter ratio (0.7≤L/D≤7.0) of the air jet. The exit geometry was found to significantly influence the entire course of propagation of the vortex ring. The orifice-generated vortex ring had superior characteristics to that produced by the nozzle under the same conditions. The vorticity generated along the wall in the orifice exit plane had a negligible effect on the circulation of the vortex ring within the specified range of Reynolds number. Compared to the nozzle-generated vortex ring, the orifice-generated ring showed reduced initial vorticity losses and less diffusive entrainment of ambient fluid. The vortex rings produced by the orifice attained more circulation, less entrainment of ambient fluid and hence rapidly propagated through longer distances in comparison to the nozzle-generated rings.     

Diffusion anisotropy in a toroidal (ring) vortex in water

Diffusion of paint (ink) particles in a toroidal (ring) vortex in a density-homogeneous liquid (water) was experimentally studied. Particle diffusion anisotropy in rotating water of the vortex was detected. The effect consists in the fact that the particle diffusivity in the direction perpendicular to the rotation axis of the torus core is much lower than that in the direction parallel to the rotation axis.     

Hopf Bifurcations,Drops in the Lid-Driven Square Cavity Flow

The lid-driven square cavity flow is investigated by numerical experiments. It is found that from $ \mathrm{Re} $$=$ $5,000 $ to $ \mathrm{Re} $$=$$ 7,307.75 $ the solution is stationary, but at $ \mathrm{Re}$$=$$7,308 $ the solution is time periodic. So the critical Reynolds number for the first Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 7,307.75 $ and $ \mathrm{Re} $$=$$ 7,308 $. Time periodical behavior begins smoothly, imperceptibly at the bottom left corner at a tiny tertiary vortex; all other vortices stay still, and then it spreads to the three relevant corners of the square cavity so that all small vortices at all levels move periodically. The primary vortex stays still. At $ \mathrm{Re} $$=$$ 13,393.5 $ the solution is time periodic; the long-term integration carried out past $ t_{\infty} $$=$$ 126,562.5 $ and the fluctuations of the kinetic energy look periodic except slight defects. However, at $ \mathrm{Re} $$=$$ 13,393.75 $ the solution is not time periodic anymore: losing unambiguously, abruptly time periodicity, it becomes chaotic. So the critical Reynolds number for the second Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 13,393.5 $ and $ \mathrm{Re} $$=$$ 13,393.75 $. At high Reynolds numbers $ \mathrm{Re} $$=$$ 20,000 $ until $ \mathrm{Re} $$=$$ 30,000 $ the solution becomes chaotic. The long-term integration is carried out past the long time $ t_{\infty} $$=$$ 150,000 $, expecting the time asymptotic regime of the flow has been reached. The distinctive feature of the flow is then the appearance of drops: tiny portions of fluid produced by splitting of a secondary vortex, becoming loose and then fading away or being absorbed by another secondary vortex promptly. At $ \mathrm{Re} $$=$$ 30,000 $ another phenomenon arises—the abrupt appearance at the bottom left corner of a tiny secondary vortex, not produced by splitting of a secondary vortex.     

Low-temperature heat transport of the zigzag spin-chain compound SrEr2O4

Low-temperature thermal conductivity ($\kappa$), as well as the magnetic properties and specific heat, are studied for the frustrated zigzag spin-chain material SrEr$_{2}$O$_{4}$ by using single-crystal samples. The specific heat data indicate the long-range antiferromagnetic transition at $\sim 0.73 $ K and the existence of strong magnetic fluctuations. The magnetizations at very low temperatures for magnetic field along the $c$ axis (spin chain direction) or the $a$ axis reveal the field-induced magnetic transitions. The $\kappa $ shows a strong dependence on magnetic field, applied along the $c$ axis or the $a$ axis, which is closely related to the magnetic transitions. Furthermore, high magnetic field induces a strong increase of $\kappa $. These results indicate that thermal conductivity along either the $c$ axis or the $a$ axis are mainly contributed by phonons, while magnetic excitations play a role of scattering phonons.     

Interactions between vortex and magnetic rings at high kinetic and magnetic Reynolds numbers

Interactions between magnetic and vortex rings are studied over a wide interval of interaction parameter values ranging from negligible magnetic effects on vorticity structure, to very strong effects. The employed interaction parameter measures the strength of the Lorentz force in units of the inertial force. At small interaction parameters, the vortex ring shapes part of the magnetic ring into a dissipative, curved, magnetic sheet structure. At high interaction parameters, the Lorentz force acts as an agent of proliferation of vortex rings, since it generates two vortex rings adjacent to the original magnetic structure, one of which is pulled (together with the advected magnetic field) into the wake of the original vortex ring, while the other escapes, ready to interact with another magnetic ring. Once within the initial vortex ring wake, both magnetic and vorticity structures are stretched into spirals, whilst the Lorentz force continuously generates new, intense vorticity at high magnetic field sites.     

Particle captured by a field-modulating vortex through dielectrophoresis force

In microfluidic technology, dielectrophoresis (DEP) is commonly used to manipulate particles. In this work, the fluid-particle interactions in a microfluidic system are investigated numerically by a finite difference method (FDM) for electric field distribution and a lattice Boltzmann method (LBM) for the fluid flow. In this system, efficient particle manipulation may be realized by combining DEP and field-modulating vortex. The influence of the density ($\rho_{\rm p}$), radius ($r$), and initial position of the particle in the $y$ direction ($y_{\rm p0}$), and the slip velocity ($u_{0}$) on the particle manipulation are studied systematically. It is found that compared with the particle without action of DEP force, the particle subjected to a DEP force may be captured by the vortex over a wider range of parameters. In the $y$ direction, as $\rho_{\rm p}$ or $r $ increases, the particle can be captured more easily by the vortex since it is subjected to a stronger DEP force. When $u_{0}$ is low, particle is more likely to be captured due to the vortex-particle interaction. Furthermore, the flow field around the particle is analyzed to explore the underlying mechanism. The results obtained in the present study may provide theoretical support for engineering applications of field-controlled vortices to manipulate particles.     

Acceleration and ejection of interacting ring vortices by radial flow

Exact solution of two-dimensional hydrodynamic equations for symmetrical configuration of four point vortices in the presence of radial flow is found. This solution describes the dynamics of a dipole toroidal vortex (consisting of two counter-rotating vortex rings) in such a flow. It is shown that in a convergent flow the ring vortices are compressed and ejected with acceleration along the symmetry axes of the system. Possible application to the problem of jets formation in active galaxy nuclei is considered.     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

气固轴对称射流中固粒扩散的研究

由三维离散涡丝方法对气固轴对称射流场数值模拟的结果表明,当固粒 Ｓｔ数＜＜１时,固粒明显受到流场运动的影响; Ｓｔ＝ １时,固粒均匀分布在涡结构周围;当 Ｓｔ ＞＞１时,固粒受流场影响较弱。对涡环沿周向施以五个波长扰动时,固粒扩散范围较宽。     

Acoustic waves emitted by a vortex ring passing near a circular cylinder

Acoustic waves emitted by a vortex ring moving near a circular cylinder have been studied experimentally and theoretically. The vortex rings used in the experiments had a translational speed ν₀ in the range 26 ⪅ ν₀ ⪅ 58 m/s and a radius of about 4·7 mm comparable in size with the cylinder radius. The acoustic pressure signals were detected by four microphones in the far field, and analyzed by digital methods. The observed pressure p obeys the scaling law p ∞ ν₀³L⁻⁴, where L is the impact distance of the vortex path to the cylinder. The observed sound wave is of dipole radiation type, and the direction of the dipole axis rotates as the vortex position changes relative to the cylinder. The direction of the dipole axis is related to that of the normal to the plane of the vortex ring. The instantaneous resultant force exerted on the cylinder by the vortex motion has also been examined, and the magnitude and the direction determined experimentally as a function of time. The theory of vortex sound predicts that the wave profile is proportional to the second time derivative of the volume flux (of a hypothetical potential flow around the cylinder) through the vortex ring. The observed scaling law and dipole directivity of the pressure are in good agreement with the theoretical predictions. The pressure profiles are calculated by using the observed vortex motion. These profiles also agree well with the observed ones, confirming the validity of the theory.     

Electronic transport through a periodic array of quantum-dot rings

Using the tight-binding approximation and the transfer matrix method, this paper studies the electronic transport properties through a periodic array of quantum-dot (QD) rings threaded by a magnetic flux. It demonstrates that the even--odd parity of the QD number in a single ring and the number of the QD rings in the array play a crucial role in the electron transmission. For a single QD ring, the resonance and antiresonance transmission depend not only on the applied magnetic flux but also on the difference between the number of QDs on the two arms of the ring. For an array of QD rings, the transmission properties are related not only to the even--odd parity of the number $N_{0}$ of QDs in the single ring but also to the even--odd parity of the ring number $N$ in the array. When the incident electron energy is aligned with the site energy, for the array of $N$ rings with $N_{0}={\rm odd}$ the antiresonance transmission cannot occur but the resonance transmission may occur and the transmission spectrum has $N$ resonance peaks ($N-1$ resonance peaks) in a period for $N={\rm odd}$ (for $N={\rm even}$). For the array of $N$ rings with $N_{0}={\rm even}$ the transmission properties depend on the flux threading the ring and the QD number on one arm of the ring. These results may be helpful in designing QD devices.     

Roles of initial condition and vortex pairing in jet noise

This is a study of the effect of initial condition on sound generated by vortex pairing in a low Mach number, cold air jet (0·15 ⩽ M ⩽ 0·35). Data has been taken, both flow velocity fields and sound pressure far fields, in a quality anechoic facility, with careful documentation of the effect of initial condition on the sound field of jets of two different geometries (i.e., circular and elliptic). Explanations are presented for most of the observed effects by applying Möhring's theory of vortex sound to vortex filament models of coherent structures in the jets. The explanations also draw upon experience with coherent structure dynamics. The sound source of interest here is that associated with the pairing of shear layer vortices. The evolution of these vortices is greatly affected by the initial condition as is their resultant sound field. The elliptic jets with laminar boundary layers show azimuthal directivity, namely, sound pressure levels in the minor axis plane were greater than in the major axis plane. This difference decreases as the nozzle boundary layer undergoes natural transition with increasing jet speed. When the nozzle boundary layer is tripped, making it fully turbulent and removing the shear layer mode of pairing, the elliptic jet sound fields become nearly axisymmetric. What appears to be the most acoustically active phase of vortex pairing has been modeled, and the resulting sound field calculated for the circular jet. Supporting evidence is found in the experimental data for the validity of this model. The model explains the connection between the initial condition and the far field sound of jets. Interestingly, a general result of Möhring's theory is that motions of vortex rings (of any arbitrary shape) can produce only axisymmetric sound fields if the rings remain in a plane. This implies that the observed asymmetric directivity of the laminar elliptic jet sound field must be due to non-planar ring motions of the vortical structures. The primary contribution of this paper is to examine quantitatively the role of vortex pairing in the production of jet noise; the results are used to reemphasize that “pairing noise” cannot be dominant in most practical jet sound fields, contrary to claims by other researchers.     

完美涡旋光中微米级粒子的受力与力矩特性分析

基于紧聚焦方法在几何焦平面处获得了完美涡旋光场,理论分析了该光场中微米级尺寸微粒受到的光学力与轨道矩.结果表明,该完美涡旋光可以在横平面上捕获微粒并驱动其绕光轴做轨道旋转运动,微粒受到的轨道矩随着拓扑荷的增大先增大后趋近于稳定.此外,分析了圆偏振、径向偏振和方位角偏振完美涡旋光对微粒施加的光学力和轨道矩.结果表明完美涡...