Row Of Vortices Research Articles

Self-propelled swimming simulations of bio-inspired smart structures

This paper presents self-propelled swimming simulations of a foldable structure, whose folded configuration is a box. For self-locomotion through water the structure unfolds and undulates. To guide the design of the structure and understand how it should undulate to achieve either highest speed or maximize efficiency during locomotion, several kinematic parameters were systematically varied in the simulations: the wave type (standing wave versus traveling wave), the smoothness of undulations (smooth undulations versus undulations of rigid links), the mode of undulations (carangiform: mackerel-like versus anguilliform: eel-like undulations), and the maximum amplitude of undulations. We show that the swimmers with standing wave are slow and inefficient because they are not able to produce thrust using the added-mass mechanism. Among the tested types of undulation at low Reynolds number (Re) regime of (Strouhal number of about 1.0), structures that employ carangiform undulations can swim faster, whereas anguilliform swimmers are more economic, i.e., using less power they can swim a longer distance. Another finding of our simulations is that structures which are made of rigid links are typically less efficient (lower propulsive and power efficiencies and also lower swimming speed) compared with smoothly undulating ones because a higher added-mass force is generated by smooth undulations. The wake of all the swimmers bifurcated at the low Re regime because of the higher lateral relative to the axial velocity (high Strouhal number) that advects the vortices laterally creating a double row of vortices in the wake. In addition, we show that the wake cannot be used to predict the performance of the swimmers because the net force in each cycle is zero for self-propelled bodies and the pressure term is not negligible compared to the other terms.

Poiseuille flow-induced vibrations of two tandem circular cylinders with different mass ratios

Flow-induced vibrations of two tandem circular cylinders with different mass ratios confined between two parallel walls are numerically studied via a lattice Boltzmann method. With fixed Reynolds number Re = 100 and blockage ratio β = 1/4, the effects of mass ratio m* = [0.0625, 16] and streamwise separation between two cylinders S/D = [1.125, 10] on the cylinder motions and vortex wake modes are investigated. A variety of distinct cylinder motion regimes involving the symmetric periodic vibration, biased quasi-periodic vibration, beating vibration, and steady regimes, with the corresponding wake structures, e.g., two rows of alternately rotating vortices, a single row of same-sign vortices, and steady wake, are observed. For each current case, the cylinder motion type is exclusive and in the binary oscillation regime, both cylinders always vibrate at a common primary frequency. The lighter cylinder usually oscillates at a larger amplitude than the heavier one, while the heavier cylinder undergoes larger lift force than the lighter one. The lift force and cylinder displacement always behave as an out-of-phase state. In the gap-interference region, large-amplitude oscillations could be produced extensively and in the wake-interference region, the cylinder motions and fluid flows are mainly dependent on the upstream cylinder. When the separation is large enough, both cylinders behave as two isolated ones. The mechanisms for the excitations of cylinder vibrations have also been analysed.

Effect of scour depth on flow around circular cylinder in gravity current

We investigated the effect of scour depth on the flow around a circular cylinder in a gravity current. In order to simulate the gravity current flow past a circular cylinder placed above a scour, we solved the incompressible Navier–Stokes and concentration transport equations based on the finite volume method. Vorticity fields, hydrodynamic forces, and pressure distributions on the cylinder and streamlines with regard to scour depth are examined to investigate the effect of scour depth on the flow over the cylinder. As the scour depth increases, the first maximum at the impact stage and mean drag during the quasi-steady state stage subsequently decrease. In particular, the first maximum drag at the impact stage is almost 2.5 times greater than the mean drag during the quasi-steady state stage, regardless of the scour depth. For a smaller scour depth, a root mean square (RMS) lift value of approximately zero reveals that no periodic vortex shedding occurs, indicating that the scour effect on vortex shedding is significant. However, as the scour depth increases, the RMS lift increases, resulting in an increase in the strength of the vortex shedding. For a larger scour depth, Kármán vortex shedding occurs near the cylinder. However, due to the existence of the scour, only negative vortices separated from the top side of the cylinder move farther downstream, resulting in a single vortex row on the smooth bed.

Orientational ordering, buckling, and dynamic transitions for vortices interacting with a periodic quasi-one-dimensional substrate

We examine the statics and dynamics of vortices in the presence of a periodic quasi-one dimensional substrate, focusing on the limit where the vortex lattice constant is smaller than the substrate lattice period. As a function of the substrate strength and filling factor, within the pinned state we observe a series of order-disorder transitions associated with buckling phenomena in which the number of vortex rows that fit between neighboring substrate maxima increases. These transitions coincide with steps in the depinning threshold, jumps in the density of topological defects, and changes in the structure factor. At the buckling transition the vortices are disordered, while between the buckling transitions the vortices form a variety of crystalline and partially ordered states. In the weak substrate limit, the buckling transitions are absent and the vortices form an ordered hexagonal lattice that undergoes changes in its orientation with respect to the substrate as a function of vortex density. At intermediate substrate strengths, certain ordered states appear that are correlated with peaks in the depinning force. Under an applied drive the system exhibits a rich variety of distinct dynamical phases, including plastic flow, a density-modulated moving crystal, and moving floating solid phases. We also find a dynamic smectic-to-smectic transition in which the smectic ordering changes from being aligned with the substrate to being aligned with the external drive. The different dynamical phases can be characterized using velocity histograms and the structure factor. We discuss how these results are related to recent experiments on vortex ordering on quasi-one-dimensional periodic modulated substrates. Our results should also be relevant for other types of systems such as ions, colloids, or Wigner crystals interacting with periodic quasi-one-dimensional substrates.

Alternating current-driven microwave loss modulation in a fluxonic metamaterial

We introduce a fluxonic metamaterial on the basis of nanopatterned superconducting Nb microstrips and employ it for modulation and synthesis of quantized loss levels in the lower GHz range by a sine-wave quasistatic ac drive. The nanopatterns are uniaxial nanogrooves with identical and different slope steepness, which induce a pinning potential of the washboard type for Abrikosov vortices. For the fundamental matching field, when the location of vortex rows geometrically matches the nanogrooves, the following effects are observed: The forward transmission coefficient S21(f) of the microstrips can be controllably modulated within a range of about 3 dB by the ac. For the sample with symmetric grooves, depending on the choice of the operation point in the current-voltage curve, the shape and the duty cycle of the output signal can be tuned. For the sample with asymmetric grooves, depending on the ac amplitude, a sine-to-triangular or a sine-to-rectangular pulse shape conversion is observed. The possibility of synthesizing quantized loss levels by a serial connection of the two samples with different nanopatterns is exemplified and can be used for the development of multilevel excess-loss-based fluxonic devices.

Analytical solutions for two hollow vortex configurations in an infinite channel

New analytical solutions for a co-travelling hollow vortex pair and a single row of hollow vortices in an infinite channel are presented. These new solutions generalise several known classical solutions for hollow vortices. The mathematical problems to be solved in each geometry are particular types of free boundary problem over a multiply connected domain. We present concise formulae for the conformal mapping determining the shape of the boundaries of the hollow vortices in both channel geometries by employing free streamline theory in combination with the function theory of the Schottky–Klein prime function. Various properties of the solutions are also presented.

A PIV study of the near wake flow features of a square cylinder: influence of corner radius

In this study, the near wake characteristics of transversely oscillating square-section cylinders with different corner radii were investigated using the particle image velocimetry (PIV) technique in a water channel with turbulence intensity of 6.5%. Five models with r/B = 0, 0.1, 0.2, 0.3, and 0.5, respectively (where r and B represent the corner radius and the characteristic dimension of the body, respectively), were studied, with the body oscillation limited to that under the lock-in condition. Corner radius was found to significantly influence the characteristics of the flow around the bodies, both under stationary and oscillating conditions. The results indicate that the Strouhal number and vortex strength of the flow increase and decrease, respectively, with an increase in the r/B ratio. The spacing between two rows of vortices (b) as well as that between consecutive vortices in a row (a) was also found to decrease with the increase in the corner radius. The b/a ratio was found to be nearly independent of the r/B ratio and body oscillation.

Mixed state and magnetization of a thin type II superconducting film in the applied parallel magnetic field: Variational technique of the inclusion of the contribution from the core of a vortex

The equilibrium vortex structure and magnetization for a thin superconducting film (with the Ginzburg-Landau parameter κ ≫ 1) in the magnetic field applied parallel to the film surface have been calculated with the inclusion of the spatial inhomogeneity of the order parameter within the core of a vortex by using a variational function. The variational approach allows obtaining more accurate values of the core self-energy in comparison to those found in the London approximation (including its changes with the growth of the vortex lattice density) and gives a more adequate picture of the interactions between vortices and of their interaction with the surface. The formula determining a correction to the London expression for the magnetic flux related to vortices in the film is derived. The comparison of the calculations performed using these two models demonstrates that the vortex core structure provides an important contribution if the film thickness is d < 50ξ. For such thin films, the novel size effect manifesting itself in a significant difference between the values of magnetization for the film and a bulk sample within the magnetic field range 0.08Hc2 < H < 0.5Hc2 has been found. It has also been demonstrated that if d decreases to d = 10ξ, the splitting of the central vortex row occurs as a second order phase transition.

AC Quantum Interference Effects in Nanopatterned Nb Microstrips

The mixed-state dc voltage response of nanopatterned Nb microstrips is investigated by combined microwave (0.5 MHz—1 GHz) and dc electrical resistance measurements. The nanopatterns are arrays of symmetric grooves on the film surface fabricated by focused ion beam milling. They provide a pinning potential of the washboard type for the vortex motion. When subject to a microwave stimulus, the dc current–dc voltage curves of the microstrips exhibit Shapiro steps. The steps occur at voltages V=n V 0=n N f Φ 0, where n is an integer, N is the number of vortex rows between the voltage leads, f is the microwave frequency, and Φ 0 is the magnetic flux quantum. These steps arise as an interference effect when one or a multiple of the hopping period of the coherently moving Abrikosov vortices coincides with the period of the ac drive. When tuning the field value away from the matching field, the steps disappear due to lacking coherence in the motion of the Abrikosov vortex lattice. Dependencies of the dc critical (depinning) current on the microwave power and frequency are reported.

Hollow vortices, capillary water waves and double quadrature domains

Two new classes of analytical solutions for hollow vortex equilibria are presented. One class involves a central hollow vortex, comprising a constant pressure region having non-zero circulation, surrounded by an n-polygonal array of point vortices with . The solutions generalize the non-rotating polygonal point vortex configurations of Morikawa and Swenson (1971 Phys. Fluids 14 1058–73) to the case where the point vortex at the centre of the polygon is replaced by a hollow vortex. The results of Morikawa and Swenson would suggest that all equilibria for will be linearly unstable to point vortex mode instabilities. However even the n = 3 case turns out to be unstable to a recently discovered displacement instability deriving from a resonance between the natural modes of an isolated circular hollow vortex. A second class of analytical solutions for periodic water waves co-travelling with a submerged point vortex row is also described. The analysis gives rise to new theoretical connections with free surface Euler flows with surface tension and, in particular, with Crapperʼs classical solutions for capillary water waves. It is pointed out that the equilibrium fluid regions found here have a mathematical interpretation as an abstract class of planar domains known as double quadrature domains.

Wall proximity effects on the effectiveness of upstream control rod

Two dimensional flow over a circular cylinder with an upstream control rod of same diameter is simulated in unbound condition and in wall bounded conditions. The cylinders are placed at various heights from the wall and the inter-distance between cylinders is also varied. The control rod is subjected to different rotation rates. It is found that, in unbound condition, rotating the control rod decreases the critical pitch length (S/Dcr) and increases the drag and Strouhal number of the main cylinder. In presence of plane wall, the shielding provided by the separated shear layers from the control rod in cavity regime is deteriorated due to deflection of shear layers which results in higher drag and large fluctuation of lift coefficient. However, in wake impingement regime, the binary vortices from the control rod are weakened due to diffusion of vorticity and hence, the main cylinder experiences a lower drag and small lift fluctuations than that of unbound condition. The critical height of vortex suppression (H/Dcr) is higher in cavity regime than that of wake impingement regime due to the single extended-bluff body like configuration. The rotation of control rod energizes the wall boundary layer and increases the critical height of vortex suppression. Increasing the rotational rate of control rod decreases the drag force and reduces the amplitude of lift fluctuation. Analysis of the wall shear stress distribution reveals that it suffers a sudden drop at moderate height where the normal Karman vortex shedding changes to irregular shedding consisting of single row of negative vortices. Modal structures obtained from dynamic mode decomposition (DMD) reveal that the flow structures behind the main cylinder are suppressed due to wall and the flow is dominated by the wake of control rod.

Waves on a Stuart vortex

We consider the linear stability of Stuart vortices, an exact periodic solution of the two-dimensional inviscid Euler equations of hydrodynamics consisting of an infinite row of co-rotating vortices, to wavelike disturbances when the vortex amplitude is small but still much larger than the disturbances. An unsteady critical layer analysis is used, with outer and inner expansions away from and near the vortex cores which we match to obtain disturbance growth rates. Disturbance-vortex interactions occur inside the critical layer and are neglected elsewhere. We consider α+-1∼O(1) and α+≈1 separately, where α+ is ratio of the disturbance wavenumber to that of the periodic vortex row. We consider primarily three-dimensional (oblique) disturbances but touch upon two-dimensional disturbances in the vortex plane. There are resonance mechanisms for oblique disturbances when k+⩽1, with k+ the ratio of the streamwise disturbance wavenumber to that of the periodic vortex row. When k+=1, this is fundamental mode or Benney–Lin instability, thought to be connected to streamwise streaks seen in experiments, and when k+=1/2, this is subharmonic instability or helical pairing, thought to be connected to vortex pairing.

Visualization of Mach waves produced by a supersonic jet and theoretical explanations

Supersonic jets emit shock waves to the outside called “Mach waves” which are long, straight and have about equal angles. Experiments done by Oertel Sen. clearly visualized these Mach waves and he showed, moreover, that such Mach waves also exist inside the jet. Measuring the Mach wave angles from many shock tube experiments revealed the existence of three wave families. They move with different speeds, denoted as w, w′ and w″, which only depend on the jet Mach number M i and the ratio a a /a i of the sound speed a a outside and a i inside the jet. For illuminating theoretically the experimental outcomes, a brand-new assumption is made which explains the three found speeds w, w′ and w″. Its central point is the production of Mach waves by two rows of vortices moving downstream inside of the jet mixing layer in two separate vortex trains. The inner vortex train creates the w′-Mach waves outside the jet and the outer vortex chain is accompanied by the w″-Mach waves towards inside the jet. Both chains form a contact surface which moves with speed w. For validating the results of the new theory the shock tube experiments are the only ones worldwide by which these three wave families have been visualized using differential interferometry: by frame series, by immobilization images and by streak records. They show density differences by light intensity variations on the image. By the immobilizations and the streak records the flow is observed through a slit on a rotating drum camera. Immobilizations use a wide opened slit and the camera turns with the speed of the Mach waves to be observed. With a narrow adjusted slit, streak records show the Mach wave traces clearly.

Simulation and Optimization of Turbine Blade Shape Modification

Thickness thinning repair analog simulated using fluid mechanics research tool ANSYS-CFX of mixed-flow turbine runner blade,Through the three-dimensional flow and numerical calculation and analysis of energy distribution on the blade after featheredging. Leaf blade repair thickness thinning after 0.5CM in the cavitation performance, vibration performance and operation performance of the performance indicators to achieve the ideal state, The new method for reducing wheel vibration, vortex row, There is a certain positive significance in improving the efficiency of turbine, make full use of new energy.

Controlled vortex motion in multiple interpenetrating pinning arrays

We study the effect of multiple interpenetrating pinning arrays on the vortex motion in the presence of an ac driving force, f d (t), by using extensive molecular dynamics (MD) simulations. Firstly, the response to a square ac wave f d (t) has been explored for the vortices interacting with a periodic square pinning array which has different pinning strengths and sizes. The effect of the type of an ac drive and its amplitude on the oscillatory dynamics of vortices have been investigated in detail. For very low displacements of the vortices, we have found that the single-particle model can produce results analytically similar to the ones obtained by the MD simulations. It is shown that the collective motion of vortices can be controlled easily by varying the number of multiple interpenetrating square pinning lattices (N SPSL). A regular sequence of peaks has been observed for N SPSL = 3 in the time evolution of the average velocity of the vortices (i.e., V x - t curves). The number of peaks (N peak) strongly depends on the magnitude of f d (t), and increases with increasing the magnitude of f d . The close relation between N peak and f d is considered as an indication of controlling vortex motion in a multiple periodic pinning structure. Finally, the variation of the power spectrum of noise S(ν) with N SPSL has been investigated. For N SPSL = 3, it has been found that the plastic motion of the row of vortices evolves at low frequencies, i.e., 1/ν behavior, whereas, at high frequencies, S(ν) shows a typical behavior of Gaussian white noise.

A ray tracing study of shock leakage in a model supersonic jet

Recent work has described screech noise from a supersonic jet as being due to leakage of a wave that is otherwise trapped in the jet's interior. In that work, the simplest of many techniques used is ray tracing for a single shear-layer modeled as a row of Stuart vortices. In the present work, a lower row of vortices is added to form a plane jet. Instead of plotting ray paths, a technique of visualization analogous to streaklines is used that better corresponds to instantaneous density fields as observed, for instance, by the Schlieren method. This produces striking images that show leakage of waves at each internal reflection resulting in a row of acoustic sources as envisioned since the 1950s. However, the sources are not isotropic and each has a zone of silence in the downstream direction. Leakage creates a fold in the wave pattern internal to the jet which leads to fine scale features. Reported experiments have also observed fine scale features (described as splitting) in the shock-cell pattern; they may be related to those observed here. Internally reflected rays also undergo a diffusive process as they propagate down the jet. In particular, each successive internal reflection at an unsteady shear-layer scatters rays along a wider range of wave angle and makes them more susceptible to leakage at the next reflection. It also causes more downstream directivity for the more downstream sources. An important result is that as the Mach number Mj is varied, maxima in leakage rate and mean acoustic amplitude occur at (near) resonances between the Mach-wave and shear-layer periods. Maxima in sound pressure level versus Mj have also been reported for laboratory round jets. Finally, as the shear-layer thickness is increased, a minimum in the rate of leakage (correlated with a minimum in radiation amplitude) occurs due to the competing effects of increased shear-layer penetration versus reduced eddy passage frequency.

樹木群を有する直線開水路流れにおける大規模水平渦の特性

The present paper is concerned with large scale vortices developing along the interface between main flow and vegetated zone in a prismatic open channel. Two types of flume experiment and LES are carried out to clarify the evolution of large vortices and to discuss the vegetation modeling. In one experiment a continuous vegetation belt stands along the centerline of the channel whereas in the other experiment patched vegetation zones are installed along the channel centerline. Flow visualization is followed by measurement of water levels and three velocity components. It is demonstrated that a row of large vortices is produced along the edge of the vegetation belt and that the large vortices survive over the gap region between the vegetation zones with active lateral mixing. LES employing the concept of vegetation density shows that it can reasonably reproduce the flow field in the vegetation zones and that further refinement is necessary for the better prediction of the flow downstream of the patched vegetation zones.

Determining the stability of steady two-dimensional flows through imperfect velocity-impulse diagrams

AbstractIn 1875, Lord Kelvin stated an energy-based argument for equilibrium and stability in conservative flows. The possibility of building an implementation of Kelvin’s argument, based on the construction of a simple bifurcation diagram, has been the subject of debate in the past. In this paper, we build on work from dynamical systems theory, and show that an essential requirement for constructing a meaningful bifurcation diagram is that families of solutions must be accessed through isovortical (i.e. vorticity-preserving), incompressible rearrangements. We show that, when this is the case, turning points in fluid impulse are linked to changes in the number of the positive-energy modes associated with the equilibria (and therefore in the number of modes likely to be linearly unstable). In addition, the shape of a velocity-impulse diagram, for a family of solutions, determines whether a positive-energy mode is lost or gained at the turning point. Further to this, we detect bifurcations to new solution families by calculating steady flows that have been made ‘imperfect’ through the introduction of asymmetries in the vorticity field. The resulting stability approach, which employs ‘imperfect velocity-impulse’ (IVI) diagrams, can be used to determine the number of positive-energy (likely unstable) modes for each equilibrium flow belonging to a family of steady states. As an illustration of our approach, we construct IVI diagrams for several two-dimensional flows, including elliptical vortices, opposite-signed vortex pairs (of both rotating and translating type), single and double vortex rows, as well as gravity waves. By also considering an example involving the Chaplygin–Lamb dipole, we illustrate how the stability of a specific flow may be determined, by embedding it within a properly constructed solution family. The stability data from our IVI diagrams agree precisely with results in the literature. To the best of our knowledge, for a few of the flows considered here, our work yields the first available stability boundaries. Further to this, for several of the flows that we examine, the IVI diagram methodology leads us to the discovery of new families of steady flows, which exhibit lower symmetry.

Instability of secondary vortices generated by a vortex pair in ground effect

AbstractIn this work, we investigate the approach of a descending vortex pair to a horizontal ground plane. As in previous studies, the primary vortices exhibit a ‘rebound’, due to the separation of secondary opposite-sign vortices underneath each primary vortex. On each side of the flow, the weaker secondary vortex can become three-dimensionally unstable, as it advects around the stronger primary vortex. It has been suggested in several recent numerical simulations that elliptic instability is the origin of such waviness in the secondary vortices. In the present research, we employ a technique whereby the primary vortices are visualized separately from the secondary vortices; in fact, we are able to mark the secondary vortex separation, often leaving the primary vortices invisible. We find that the vortices are bent as a whole in a Crow-type ‘displacement’ mode, and, by keeping the primary vortices invisible, we are able to see both sides of the flow simultaneously, showing that the instability perturbations on the secondary vortices are antisymmetric. Triggered by previous research on four-vortex aircraft wake flows, we analyse one half of the flow as an unequal-strength counter-rotating pair, noting that it is essential to take into account the angular velocity of the weak vortex around the stronger primary vortex in the analysis. In contrast with previous results for the vortex–ground interaction, we find that the measured secondary vortex wavelength corresponds well with the displacement bending mode, similar to the Crow-type instability. We have analysed the elliptic instability modes, by employing the approximate dispersion relation of Le Dizés &amp; Laporte (J. Fluid Mech., vol. 471, 2002, p. 169) in our problem, finding that the experimental wavelength is distinctly longer than predicted for the higher-order elliptic modes. Finally, we observe that the secondary vortices deform into a distinct waviness along their lengths, and this places two rows of highly stretched vertical segments of the vortices in between the horizontal primary vortices. The two rows of alternating-sign vortices translate towards each other and ultimately merge into a single vortex row. A simple point vortex row model is able to predict trajectories of such vortex rows, and the net result of the model’s ‘orbital’ or ‘passing’ modes is to bring like-sign vortices, from each secondary vortex row, close to each other, such that merging may ensue in the experiments.

Skyrmion rows, vortex rows, and phase slip lines in sheared multi-component condensates

When a condensate is sheared by imparting a velocity to a part of the condensate, phase singularities must appear at the interface between the region that is still at rest and the region that has acquired a velocity. For helium, Feynman argued that these phase singularies will arrange themselves in the form of a vortex row. Bose–Einstein condensates of ultracold atomic gases differ from helium in that the healing length is generally much larger and is, in fact, tunable. Another difference is that multicomponent condensates can be created, where the two components forming the mixture are usually two different hyperfine states of the condensed atoms. These two components can be manipulated separately and can be interconverted. In this contribution, we investigate how these additional degrees of freedom, available in quantum gases, change what happens in sheared condensates. In particular, we consider skyrmion rows as an alternative to vortex rows, and we also consider phase slip lines filled with the second, unmoving component, in a condensate mixture. We show that depending on the ratios of the interaction strengths between the components, and depending on the shear velocity, skyrmion rows and phase slip lines can become lower in energy than vortex rows, and hence should be observable in quantum gases. Moreover, we find that the velocity field affects the stability region of the condensate with respect to phase separation.