Behaviour of spiral vortices on a rotating cone in axial flow

Summary The purpose of the present paper is to investigate experimentally in detail the boundary layer transition process and the behaviour of spiral vortices appearing in the transition range of the boundary layer on a 30°-cone, rotating in axial flow. Counterrotating spiral vortices in the transition range are visualized with a white smoke method, and observed the time dependent behaviour of them using a drum camera and a light sheet illumination method with a stroboscope flash light. The light passes a slit in order to illuminate only a thin sheet in the flow. With this method, the time dependent growing up and breaking down process of these spiral vortices is greatly clarified. A hot wire anemometer is also used for measuring in the flow field quantitatively. The results show that the spiral vortices are generated in the thin region of the steep shear velocity gradients near the wall. As the vortices grow up in z-direction, they are strongly distorted by the mean velocity field there, and finally they are teared off.With 7 Figures     

Instability of Quantized Vortices Attached to Oscillating Boundaries in Superfluid 4He

The motion of quantized vortices is studied using a vibrating wire in superfluid ⁴He. A vortex filtering method provides a superfluid practically free of remanent vortices in which the vibration of a wire cannot generate turbulence. Vortex lines are produced by cooling through the superfluid transition and remain forming bridges between a wire and a surrounding wall. Bridged remanent vortices increase the resonance frequency of a vibrating wire: the rate of an increase due to the remanent vortices is constant in a laminar flow regime and steeply increases in a turbulent flow regime with increasing wire velocity. These results suggest that oscillation of the bridged vortices provides a linear contribution to the wire vibration in the laminar flow regime, until instability occurs in the oscillation of the vortices, causing turbulence.      

Rotating-disk-type flow over loose boundaries

Rotating-disk-type flow of a liquid over a loose boundary, such as a layer of sand, is investigated. For this flow the formation of a new large-scale spiral pattern has been discovered. The new pattern is reminiscent of the Type-I spiral-vortex structures which characterize the laminar–turbulent transition region of boundary layers over rigid rotating disks. Flow visualizations reveal that the new pattern and the Type-I spiral vortices co-exist in the loose-boundary flow. The research investigating the origin of the new large-scale pattern is reviewed. Then photographs from flow visualizations are analysed to obtain estimates for the critical Reynolds number for which Type-I spiral vortices first appear for the loose-boundary flow and for the critical Reynolds numbers for the laminar–turbulent transition of the boundary layer. The results suggest that Type-I vortices appear at much lower Reynolds numbers over loose boundaries in comparison with flow over rigid rotating disks and that transition also appears to be advanced to much lower Reynolds numbers. The discussion of the results suggests that advanced transition arises from disturbances introduced into the flow after the loose boundary has been mobilized and not from disturbances associated with the roughness that the surfaces of the granular layer represents to the flow while grains are at rest.     

Stability of the boundary layer on a sphere rotating in still fluid

Summary A theoretical study of the transition of a three-dimensional boundary layer on a sphere rotating in still fluid is carried out by a linear stability analysis. A set of perturbation equations governing the instability of the flow field is derived assuming the perturbations to be consisting of spiral vortices. It is shown that the critical Reynolds numbers obtained in the present analytical study are close to those observed in experiments. It has been found that the streamline-curvature instability appears in the rotating sphere flow. It is also shown that the cross-flow instability is dominant near the poles of a sphere while the streamline-curvature instability overtakes near the equator.     

High-power efficient multiple optical vortices in a single beam generated by a kinoform-type spiral phase plate

We propose using a solitary kinoform-type spiral phase plate structure to generate an array of vortices located in a single beam. Kinoform-type spiral surfaces allow each wavelength component of the phase modulation value to be wrapped back to its 2 pi equivalent for optical vortices of high charge. This allows the surface-relief profiles of high-charge vortices to be microfabricated with the same physical height as spiral phase plates of unity-charged optical vortices. The m-charged optical vortex obtained interacts with the inherent coherent background, which changes the propagation dynamics of the optical vortex and splits the initial m charge into /m/ unity-charged optical vortices within the same beam. Compared to a hologram, a multistart spiral phase plate is more efficient in the use of available spatial frequencies and beam energy and also is computationally less demanding. Furthermore, using microfabrication techniques will allow for greater achievable tolerances in terms of smaller feature sizes.     

Current–Voltage Measurements on a Bi2Sr2CaCu2O x Whisker and Investigation of Its Vortex Dynamics in Self Field

We report current–voltage measurements carried out on a high quality Bi₂Sr₂CaCu₂O _x whisker in a large temperature range below the critical temperature. When a perpendicular field is applied, the current–voltage curves are typical of the flux flow regime at low fields and resemble flux creep characteristics at high fields. This change, related to what is described as the critical current peak effect is associated to a transition between different vortex phases. In this contribution, we focus on the dynamics of the vortices in self field. We show that the critical current in the flux flow regime can be calculated straightforwardly taking into account inter-vortex forces only, supposing that free vortices run between pinned vortices.     

Self-Organized Superfluid States in Gravity and Heat Flow

When ⁴ He is heated from above near the superfluid transition, there can appear a self-organized region, either in normal fluid or superfluid, with the temperature gradient equal to the transition temperature gradient. When it is in a superfluid state, there can be two regimes. Regime M is realized relatively far from the superfluid transition, where thermal resistance due to vortices is described in terms of the conventional Gorter–Mellink mutual friction. In regime G vortices are densely generated, where the line density in units of ^–2 is much larger than in any other previous experiments. Such a self-organized superfluid can coexist with a normal fluid or a superfluid containing only a small number of vortices in a dynamical steady state.     

Spiral vortices in boundary layer transition regime on a rotating disk

Summary Behavior of spiral vortices on a disk rotating in still fluid is studied theoretically and experimentally in detail. A linear stability analysis, in which effects of streamline curvature and Coriolis force are considered, gives a critical Reynolds number at the onset of instability close to the one measured here by using a hot wire probe. Gradient of the vortex axis is determined under a condition of the maximum amplification. Flow patterns in the transition regime are experimentally visualized. The results show that the number of the spiral vortices is 31 or 32 as mean value and the gradient of the vortex axis decreases from 14° to 7° as the local Reynolds number is increased.

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Spiral-Wirbel im Umschlagbereich der Grenzschicht an einer rotierenden Scheibe

Zusammenfassung Das Verhalten der spiralen Wirbel an einer in ruhender Flüssigkeit rotierenden Scheibe wird theoretisch und experimentell eingehend untersucht. Eine lineare Stabilitätstheorie, in welcher der Einfluß von Krümmung der Stromlinien und Coriolis-Kraft in Betracht gezogen wird, ergibt eine kritische Reynolds-Zahl des Indifferenzpunktes, die gut mit dem mit einem Hitzdrahtgerät gemessenen Wert übereinstimmt. Der Gradient der Wirbelachse wird unter der Bedingung der maximalen Anfachung bestimmt. Der Strömungsvorgang im Umschlagbereich wird experimentell sichtbar gemacht. Dadurch ergibt sich, daß die Anzahl der an der Scheibe auftretenden Wirbel 31 oder 32 im Mittel beträgt, und der Gradient der Wirbelachse mit zunehmender lokaler Reynolds-Zahl von 14° bis zu 7° abnimmt.

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With 12 Figures

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Dedicated to Professor Dr. Henry Görtler on the occasion of his seventieth birthday     

Recognition of the interference spiral image in a fiber optical sensor employing optical vortices

Three methods of processing the image of an interference spiral formed in a fiber optical sensor employing optical vortices have been considered. It is established that a method based on recognition of the spiral image is most stable with respect to noises. Using this technique, it is possible to determine the angle of spiral rotation even when the visibility of the interference pattern decreases to 0.2. The passage from intensity measurements to determination of the geometric parameters of the image significantly increases the range of linearity of interferometric devices employing optical vortices.     

Transition from Taylor vortices to cross-flow instabilities

Summary We present experimental results of fluid flow instabilities between different rotating surfaces. We start withcounter-rotating Taylor vortices between two coaxial cylinders. We go over to rotating cones with increasing apex angle. Due to the growing cross-flow we finally end up with spiral vortices allrotating in the same direction between a rotating disk and a housing. Figure 13 gives a complete survey of these results. We discuss the transition from one vortex system to the other in detail.Dedicated to Prof. Dr. Dr. h. c. mult. S. Wittig on the occasion of his 60th birthday     

Precessing Vortex Motion and Instability in a Rotating Column of Superfluid 3He-B

In a rotating circular cylinder of superfluid ³He-B, an evolving vortex expands longitudinally such that its end point describes a helically spiralling trajectory along the cylinder wall. The spiral motion is found to give rise to a periodically oscillating NMR signal, which is brought about by the modulation in the superfluid counterflow and its influence on the “flare-out” order parameter texture. The new NMR signal becomes observable within a narrow temperature interval close to the onset temperature of turbulence, when new vortices are continuously generated by the single-vortex instability at the cylindrical wall at a slow rate, ～1 vortex/s. We use numerical vortex filament calculations to examine the precessing motion of the evolving vortices, while they expand towards their stable state as rectilinear line vortices.     

The growth of Görtler vortices in compressible boundary layers

The linear instability of Görtler vortices in compressible boundary layers is considered. Using asymptotic methods in the high-wavenumber regime, it is shown that a growth-rate estimate can be found by solving a sequence of linear equations. The growth rate obtained in this way takes non-parallel effects into account and can be found much more easily than by ordinary differential equation eigenvalue calculations associated with parallel-flow theories.     

On the development of Görtler vortices in wall jet flow

The development of Görtler vortices in wall jet flow over curved surfaces is considered in both the linear and nonlinear growth régimes. It is shown, using asymptotic methods based on the largeness of the wavenumber of the vortices, that this hydrodynamic instability is prone to occur more readily on concave rather than convex surfaces. It is found that after passing the position of neutral stability, the flow develops a surprising structure quite unlike that produced in the Blasius boundary-layer. Once the flow is into the unstable regime, the effect of increasing the Görtler number is to move the vortices away from the wall.     

Generation of high-order optical vortices using directly machined spiral phase mirrors

We report on the generation of high-order optical vortices by spiral phase mirrors (SPMs). The mirrors are produced by direct machining with a diamond tool and are shown to produce high-quality optical vortices with topological charges ranging from 1 to upwards of 100 at a wavelength of 532 nm. The direct machining technique is flexible and offers the promise of high-precision, large-diameter SPMs that are compatible with high optical powers.     

Nanostructure of vortex during explosion welding

The microstructure of a bimetallic joint made by explosion welding of orthorhombic titanium aluminide (Ti-30Al-16Nb-1Zr-1Mo) with commercially pure titanium is studied. It is found that the welded joint has a multilayered structure including a severely deformed zone observed in both materials, a recrystallized zone of titanium, and a transition zone near the interface. Typical elements of the transition zone-a wavy interface, macrorotations of the lattice, vortices and tracks of fragments of the initial materials-are determined. It is shown that the observed vortices are formed most probably due to local melting of the material near the contact surface. Evidence for this assumption is deduced from the presence of dipoles, which consist of two vortices of different helicity and an ultrafine duplex structure of the vortex. Also, high mixing of the material near the vortex is only possible by the turbulent transport whose coefficient is several orders of magnitude larger than the coefficient of atomic diffusion in liquids. The role played by fragmentation in both the formation of lattice macrorotations and the passage of coarse particles of one material through the bulk of the other is determined.     

Capture of convective vortices by an unsteady-state flow in a Hele-Shaw cell

The specific transient regime of thermal convection in a Hele-Shaw cell has been studied experimentally and theoretically. It is a kind of unsteady-state, four-vortex flow, symmetric about the vertical axis, in the form of periodic pulsations of the lower convective cells, with the latter being partially adsorbed by the upper vortices. The transient pulsational regimes in a Hele-Shaw cell were revealed experimentally in studying convective motions in a transformer oil. These pulsational flows are unstable and with time they are always rearranged into a steady four-vortex vibrational regime with reconnection of corner vortices. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 1, pp. 100–106, January–February, 2007.     

Depinning at the initial stage of the resistive transition in superconductors with a fractal cluster structure

The effects of the initial dissipation of the energy in a superconductor containing fractal clusters of a normal phase are considered. In the interval of currents preceding the resistive transition, an increase in the fractal dimension of clusters leads to an increase of the sample resistance and widening of the region of initial dissipation in the current-voltage characteristic. This is caused by an increase in the density of free vortices broken away from the pinning centers when the current flows. Dependences of the density of vortices on the fractal dimension of cluster boundaries are found for various values of the transport current.     

COAGULATION OF SUSPENDED PARTICLES BY BROWNIAN MOTION FOR THE QUASI-SELF-PRESERVING CASE

An analytic solution is developed for the aerosol coagulation problem in the transition regime. The size distribution of a coagulating aerosol is represented by log-normal functions and particle size distribution is assumed 10 pass through a series of quasi-self-preserving size distributions. The effects of Knudsen number on the Brownian coagulation are discussed along with the results. It is confirmed that after a sufficient period of elapsed time, a self-preserving log-normal size distribution develops whose geometric standard deviation remains unchanged. Such a distribution is found to be narrower than that for the continuum regime and depends upon the Knudsen number. It is shown that the current model serves as the upper bound for the transition regime coagulation problem while the continuum regime constitutes the lower bound. Good agreement was obtained when the present analytic solution was compared with existing numerical studies on transition regime coagulation for the regime up to the Knudsen number of about 1.     

Liquid 4He: Contributions to First Principles Theory. I. Quantized Vortices and Thermohydrodynamic Properties

Quantized vortices in liquid ⁴ He are treated quantum mechanically with realistic many-body model wave functions in variational calculations for energy and core structure at T = 0 K. A rectilinear vortex and both small and large vortex rings are studied. Calculated results indicate that rotons are not just small-quantized vortex rings. We compare our results for quantized vortices with experimental data and with theoretical results calculated by others. Correlated basis functions and standard statistical mechanics are used in treating thermohydrodynamic properties of flowing liquid ⁴ He. The Helmholtz potential is evaluated for a model of the flowing liquid that includes phonons and interacting rotons. Characteristics of this potential are discussed. The physical nature of negative superfluid density is explained. Superfluid density, entropy, and specific heat for liquid He-II are evaluated using our theory and the results are compared with experimental data. Very good agreement is found, except in a small temperature range near the λ transition. We indicate that results obtained here can be used in extending the theory to include thermally excited vortices and to investigate the possible role of vortices in accounting for the λ transition in liquid ⁴ He.      

Production and characterization of spiral phase plates for optical wavelengths

We describe the fabrication and characterization of a high-quality spiral phase plate as a device to generate optical vortices of low (3-5) specified charge at visible wavelengths. The manufacturing process is based on a molding technique and allows for the production of high-precision, smooth spiral phase plates as well as for their replication. An attractive feature of this process is that it permits the fabrication of nominally identical spiral phase plates made from different materials and thus yielding different vortex charges. When such a plate is inserted in the waist of a fundamental Gaussian beam, the resultant far-field intensity profile shows a rich vortex structure, in excellent agreement with diffraction calculations based on ideal spiral phase plates. Using a simple optical test, we show that the reproducibility of the manufacturing process is excellent.