line of Eq. (12) exceeds the velocity of sound. This may result in the Vavilov-Cherenkov damping. We leave this problem for a separate work. The kinetic term becomes strongly modiﬁed due to the exchange of ﬂuctuations. The ring **vortex** **motion** due to the term [ ˙ X × X ] in the medium consisting of the charged scalar ﬁeld condensate is possible. The interaction with the fermion asymmetric back- ground results in additional term [X × X ] in equation of **motion** because of the anomalous current

The dynamics of vortices in Gross–Pitaevksii equations have been the subject of much study in the past few decades. The connection between the **vortex** **motion** in superfluids, where p(x) ≡ 1, and simplified ODEs was made by Fetter in [11], and it was shown that vortices interact with each through a Coulomb potential. On the other hand, in BECs with nontrivial trapping potentials, p(x) = O(1), it was shown by Fetter and Svidzinsky in [12] that vortices interact solely with the background potential and are carried along level sets of the Thomas–Fermi profile.

30 Read more

In practice, it is not feasible to use this model directly to simulate the response of a macroscopic superconducting sample because of the vast number of vortices typically found inside such samples. This has led to the search for an averaged model of supercon- ducting **motion** which is capable of giving an approximate description of the **motion** of large numbers of vortices. Modelling of this form was ﬁrst conducted by Brandt [5] on the basis of heuristic arguments. A subsequent formal derivation of an averaged model from (1.1)–(1.2) was made by Chapman [6] in a regime where vortices are suﬃciently densely packed, and the magnetic ﬁelds correspondingly large, so that the the ﬁrst term on the right of (1.1) can be neglected. In certain special geometries, such as thin ﬁlms, this turns out to be a reasonable assumption however in most three-dimensional situations such an assumption leads to a model which is linearly ill-posed [20]. The reason for this pathological behaviour is a three-dimensional **vortex** instability that occurs wherever there is a component of ∇ ∧ H in the direction of the **vortex** tangent t; this instability was ﬁrst noted by Clem [11]. Over a short time scale, the instability causes **vortex** lines to develop a highly curved spiral structure which invalidates the assumption that the second term on the right-hand side of (1.1) is much larger than the ﬁrst. A more detailed investigation, carried out in earlier work [18], reveals that the instability grows so as to try to align the **vortex** tangent perpendicular to the local electric current density j = ∇ ∧ H or, taking an alternative viewpoint, that the resulting **vortex** **motion** causes an electric ﬁeld parallel to the current density j.

37 Read more

Experimental evidence for the generation of **vortex**-like structures in shallow water has been given by Oltman-Shay, Howd & Birkemeier (1989) who studied the effect of a current flowing along a beach. Evidence for the generation of vortices (in shallow water) by flow round an obstacle can be found in Van Dyke (1982) which contains an aerial photograph of the flow around a grounded tanker. The marker used to visualize the flow is the oil seeping from the tanker. In Hamm, Masden & Peregrine (1993) observations of an intermittent rip current consisting of **vortex** pairs propagating seaward is reported. They also remark upon the difficulty of observing large-scale flows without the presence of a marker, such as oil or sediment. Such difficulties led Couder & Basdevant (1986) to experimentally investigate two-dimensional high Reynolds number flows in a soap film forced by a moving disc. The results of this experiment show the generation of coherent vortices and **vortex** couples.

24 Read more

Figs. 3 and 4 show a comparison between the **vortex** ﬂow ﬁeld as predicted by the standard k e model and R e /k e against experimental measurements. The axial velocity predictions of the two models are close, and both models over-pre- dict the axial velocity near to the outer wall. This can be attributed to the complexity of the ﬂow near to the wall, and also to the unsteadiness of the **vortex** breakdown region where the measurements plotted in Figs. 3 and 4 were conducted. Such region exhibits a sharp drop in the **vortex** strength, as it is shown later in this article. The standard k e model, however, fails to predict the **vortex** **motion** compared to the R e /k e model as shown in Fig. 4. The additional term in the e equation of the R e /k e model damps the dissipation rate predictions by the standard model, in order to take into account the effect of elevated strain rates produced by anisotropic turbulence inherited by swirling ﬂows. This produces enhanced predictions of the forced **vortex** ﬁeld, which complies with the theory of postulates that forced **vortex** regime produces a stabilizing effect on the turbulence ﬁeld [53,54].

13 Read more

Conclusion. Application of the “elliptic approach” [4] to studying evolution of a single synoptic **vortex** on the ß-plane has permitted to generalize the earlier- proposed theory by supplementing balance of the forces influencing the **vortex** with the inertial summands. It is shown that the deduced evolution equations are of the Hamiltonian form in case the non-canonical character of the used set of va- riables is taken into account. The evolution equations describing the **vortex** core and the trap zone center **motion** for a particular case of the initially circular **vortex** with constant vorticity, are written in two ways: the “Lagrangian” form (the va- riables are the trap zone vorticity, and the coordinates of the **vortex** core and the trap zone center) and the “Euler” one (the variables are the **vortex** **motion** velocity components and the trap zone vorticity). Analysis of the “Lagrangian” solution permits to interpret the **vortex** self-propagation on the ß-plane without basing on the force balance. It is revealed that the **vortex** core and the trap zone centers are displaced along the meridian; and their synchronous movement is similar to trans- lation of a pair of point vortices with identical intensity but different signs.

The radial clearance C of the screw conveyor was chosen to be at least 1.5 times larger than the maximum particle size in order to prevent jamming of particles in the clearance space leading to particle attrition and increased energy loss. Also research has shown that the throughput of an enclosed screw conveyor is influenced by the rotational or **vortex** **motion** of the bulk material during transportation and degree of fill or fullness of the screw [11, 12]. As the rotational speed of the conveyor increases, the rotational or **vortex** **motion** decreases (up to a limiting value) making for a more efficient conveying action. But in the centrifuge the conveying action is low

Tarbela dam is one of the largest earth filled dam in the world used for power generation and irrigation pur- poses. Like all reservoirs the sediments inflow in the Tarbela reservoir has resulted in reduction in water storage capacity and is also causing damage to the tunnels, power generating units and ultimately to the plant equipment. This numerical study was performed to predict the flow patterns and characteristics in Tarbela dam. Tunnel 3 and 4 inlets; originally on the bed level were raised in the 3-D model and meshed. Analysis was performed using multiphase flow (water and air) for maximum inflow in the reservoir, i.e., considering summer season and discharging water through different locations, i.e., tunnels and spillways. Pressure, ve- locities, flow rate and free surface height results obtained were found in good agreement with the analytical and existing results where available. Results show uneven discharge through each gate due to maximum ve- locity near exits and overall stagnant phenomena of water within the reservoir. Maximum velocity was ob- served along the spillways outlet. Strong **vortex** **motion** was observed near the spillways outlet and tunnel inlets. New design of Tunnels 3 and 4 were suggested to WAPDA in order to decrease the sediment inflow and improvements in design of the spillways were suggested.

In this experiment, the intake air is seeded with fine oil droplets that do not modify the fluid properties while being able to track accurately the fluid **motion**. The illumination source is a copper vapor laser (ACL 45W Oxford Laser). This laser is pulsed with an adjustable repetition rate up to 10 kHz. Mean pulse energies are 6.5 mJ at wavelengths of 510.6 nm and 578.2 nm and their duration lies between 10 ns and 60 ns. A 35 mm drum camera (CORDIN 350) viewing perpendicular to the laser sheet records light scattered by seeding particles with an acquisition rate up to 8000 frames/s. The film type is ILFORD HP5+, developed to its nominal speed of 400 ASA with KODAK TMAX developer. To extract quantitative information from images of particle on the negative, a high-resolution film scanner (KODAK RFS 2035) is used. To apply a cross-correlation approach, concerns peculiars to film support and the digitalization stage have to be taken into account. A special film holder was designed to fit in the scanner in order to translate the film accurately and to press it between two strip of glass. Each image of particle on the film was digitized in 8 bits with a 2000 dpi spatial resolution. Each image consists in 1400x1050 pixels with a resolution of approximately 20 pixels/mm.

11 Read more

To understand its complex orbital cycle, we separate the par- ticle **motion** into inward and outward phases. In the initial state, the microparticle is trapped at the Bessel annular beam (z = 30 µm) which has the maximum beam intensity in the field. OAM with a topological charge ` = 15 is encoded onto both the Bessel and the perfect **vortex** beams by the SLM, which is transferred to the microparticle via light scattering and sets the microparticle into rotation. Depending on the topological charge of the beam and the orbital rate and the orbital radius of the particle, the inertial force (centrifugal in this case) increases the orbital radial position with respect to the radial trap. However, the particle only remains trapped while the orbital frequency is lower than the trap frequency, i.e. once the inertial force exceeds the radial trapping force, the particle is horizontally launched into free space (outward phase) and falls due to gravity, until the force due to the perfect **vortex** beam (r = 25 µm; z = 0 µm) provides sufficient levitation. Due to both the scattering and gradient forces acting on the particle, it is guided along the beam

and made flat prior to each repeat. Once the appropriate stroke time for critical conditions had been identified, the velocity field of the corresponding **vortex** ring was measured using particle imaging velocimetry (PIV), the details of which are given below in Sec. II B. Note that the PIV data captured the ring flow-field over the entire impact region, and at each stage during the interaction. To minimise the experimental errors associated with the incremental increase of the pump stroke time, the entire procedure described above was repeated several times (for each sediment type and bed slope) so that an average could be taken. The velocity data were also used to directly measure U and D for each **vortex** ring (from the period before the ring’s trajectory was affected by the sediment layer). The values of U and D reported here are the corresponding averages obtained from the repeated experiments, which had typical variability of ±6% and ±4%, respectively. Over the range of critical impact conditions analysed in this article, the corresponding **vortex** ring Reynolds number, Re = UD/ν, was varied between 450 and 3360 (where 0.8 ≤ D/D 0 ≤ 1.2).

23 Read more

The problem of a pair of point vortices impinging on a ﬁxed point **vortex** of arbitrary strengths [E. Ryzhov and K. Koshel, EPL 102, 44004 (2013)] is revisited and investi- gated comprehensively. Although the **motion** of pair of point vortices is established to be regular, the model presents a plethora of possible bounded and unbounded solutions with complicated **vortex** trajectories. The initial classiﬁcation [E. Ryzhov and K. Koshel, EPL 102, 44004 (2013)] revealed that pair could be compelled to perform bounded or unbounded **motion** without giving a full classiﬁcation of either of those dynamical regimes. The present work capitalizes upon the previous results and introduces a ﬁner classiﬁcation with a multitude of possible regimes of **motion**. Regimes of bounded **motion** for the **vortex** pair entrapped near the ﬁxed **vortex** or of unbounded **motion**, when the **vortex** pair moves away from the ﬁxed **vortex**, can be categorized by varying the two governing parameters: (i) the ratio of the distances between pair’s vortices and the ﬁxed **vortex**, and (ii) the ratio of the strengths of the vortices of the pair and the strength of the ﬁxed **vortex**. In particular, a bounded **motion** regime where one of pair’s vortices does not rotate about the ﬁxed **vortex** is revealed. In this case, only one of pair’s vortices rotates about the ﬁxed **vortex**, while the other one oscillates at a certain distance. Extending the results obtained with the point-**vortex** model to an equivalent model of ﬁnite size vortices is the focus of a second paper.

31 Read more

geometry arises as the infinite electric charge limit of a certain semi-local **vortex** model [3, 12], so the RMG flow may be relevant to the low energy dynamics of such vortices in the presence of a Chern-Simons term. However, our main interest in it concerns the question of completeness. Since RMG flow proceeds with constant speed, it is immediate that RMG flow on any geodesically (or, equivalently, metrically) complete k¨ahler manifold is complete, that is, given any initial data x ∈ M , v ∈ T x M, there is a corresponding RMG curve α : R → M (well-

29 Read more

Muskrats and ducklings employing a drag-based propulsion mode use a specific stroke angle for a given body speed (Fish, 1984; Algeldinger and Fish, 1995). Our experiment to find the optimal stroke angle was meant to investigate an important flow phenomenon that can influence a preferred stroke angle. From repeated paddling motions of the propulsor, it has been observed that the ring-like **vortex** structure is shed into the wake (Algeldinger and Fish, 1995; Drucker and Lauder, 1999). The closed **vortex** structure in the wake originates from a starting **vortex** (a tip **vortex** and side-edge vortices in our case) and a stopping **vortex**. When the propulsor decelerates its power strokes, the stopping **vortex** starts to shed from the plate. The shedding process continues even after the propulsor finishes its power stroke. How the stopping **vortex** is shed depends on the shape and flexibility of the plate and the angular velocity program. For example, the stopping **vortex** sheds smoothly for the sinusoidal velocity program whereas it sheds abruptly for the trapezoidal velocity program because of its short deceleration time.

Experiments have been conducted to investigate the two-degree-of-freedom **vortex**-induced vibration (VIV) response of a rigid section of a curved cir- cular cylinder with low mass-damping ratio. Two curved configurations, a concave and a convex, were tested regarding the direction of the flow, in addition to a straight cylinder that served as reference. Amplitude and frequency responses are presented versus reduced velocity for a Reynolds number range between 750 and 15,000. Results for the curved cylinders with concave and convex configurations revealed significantly lower vibra- tion amplitudes when compared to the typical VIV response of a straight cylinder. However, the concave cylinder showed relatively higher amplitudes than the convex cylinder which were sustained beyond the typical synchro- nisation region. We believe this distinct behaviour between the convex and the concave configurations is related to the wake interference taking place in the lower half of the curvature due to perturbations generated in the hor- izontal section when it is positioned upstream. Particle-image velocimetry (PIV) measurements of the separated flow along the cylinder highlight the effect of curvature on **vortex** formation and excitation revealing a complex fluid-structure interaction mechanism.

28 Read more

We consider the positions and velocities of electrons and spinning nuclei and demonstrate that these particles harbour hidden momentum when located in an electromagnetic field. This hidden momentum is present in all atoms and molecules, however it is ultimately canceled by the momentum of the electromagnetic field. We point out that an electron **vortex** in an electric field might harbour a comparatively large hidden momentum and recognize the phenomenon of hidden hidden momentum.

In the present work, a TDOF riser model with internal pressure variation was studied and the corresponding **vortex** shedding pattern was analyzed.Also, different hydrodynamic characteristics of riser like lift and drag forces were calculated in ANSYS FLUENT. The vortices evoked from behind the cylinder, at the wake portion was very much distinct in the case of riser without internal pressure. Drag coefficient showed a higher value for 60 Pa and lift coefficient was higher for 80Pa.The frequency of oscillations was calculated for one cycle and was found to increase with increase in fluid pressure. Also, at 70 Pa pressure, the cylinder shows a tendency to beat at a reduced velocity of Ur=5 and a mass ratio of 0.55.At 70 Pa pressure, the riser is observed to oscillate in the CF direction with a frequency equal to the **vortex** shedding frequency. As a result of which synchronization region is developed and together they resonate which results in failure of the riser system.

Once a **vortex** ring is constructed by the method of the previous section, we have available an exact solution of the Euler equations of incompressible, inviscid ow. We can predict the behavior of disturbances to this exact solution by numerical simulations, as described subsequently, or by analytical treatment of instabilities. Although there has been considerable research on the stability of thin rings, little is known about the stability of exact rings with swirl. In this section we discuss the stability of general **vortex** rings using a WKB type method developed by Lifschitz and Hameiri 12, 13, 14, 15], valid for short wavelengths and small amplitude perturbations. Once the growth rates of these instabilities have been calculated, we can compare them with the results of time-dependent numerical simulations. This gives us an opportunity to determine the general applicability of the WKB method.

11 Read more

components) and axi-symmetric (Fig. 5). The three- dimensional character of the flow is the result of the imbalance of the centrifugal forces in the annulus: indeed, the linear variation of the radius versus the conical axial position z induces a linear variation of these centrifugal forces. The flow observed in any azimuthal plane corresponds to a large loop going up along the inner cone and down along the outer cone and turning at the end plates [1]. These end plates being fixed with no-slip conditions, the centrifugal forces decrease in their vicinity. This effect will promote end recirculations, in the direction of the main loop at the bottom and in the opposite direction at the top. The recirculation at the bottom will only reinforce the main loop. In contrast, the recirculation at the top will progressively generate a **vortex** in counter-rotation with the main loop. Due to the axi-symmetry of the flow, this **vortex** (known as Ekman **vortex**) is in fact a toroidal cell. In the small gap situations considered here, it has not been possible to provide evidence of this Ekman **vortex**.

This is a wind generator without blades. Instead of capturing energy via the rotational **motion** of a turbine the **Vortex** takes advantage of what’s known as vortices an aerodynamic effect that occurs when wind breaks against a solid structure[1] .By this project, we are going to generate electricity by using the bladeless windmill. This wind mill will have no blades. It will generate electricity by using oscillation due to wind. It works on principle of electromagnetic induction or vibrations. Here, electricity can be generated by using linear alternator or piezoelectric material. The kinetic energy is converted into electricity by an alternator to improve the efficiency of the energy being gather working on a wind turbine that operates on the principle of vortices an aerodynamic effect of wind that turns wind into kinetic energy that can be used as electricity. The advantages of this turbine over our present ones are: there are no gears, bolts or mechanical moving parts so they are cheaper to manufacture and maintain. It would cost less than the conventional turbine with its major costs for the blades and support system.