Showing papers on "Vortex published in 1991"

Quantized Vortices in Helium II

Abstract: Preface 1. Background on classical vortices 2. Background on liquid helium II 3. Vortex dynamics and mutual friction 4. The structure of quantized vortices 5. Vortex arrays 6. Vortex waves 7. Quantum turbulence 8. Nucleation of quantized vortices Index.

Unified theory of effects of vortex pinning and flux creep upon the rf surface impedance of type-II superconductors.

Abstract: We present a new theoretical approach that permits the rf surface impedance ${\mathit{Z}}_{\mathit{s}}$ of type-II superconductors to be calculated over a wide range of angular frequencies \ensuremath{\omega}, magnetic inductions B, and temperatures T. Our approach, based on a self-consistent treatment of vortex dynamics, includes the influence of both vortex pinning and flux creep upon ${\mathit{Z}}_{\mathit{s}}$ in a unified manner, by making use of continued-fraction-expansion results for the dynamic mobility of a particle undergoing Brownian motion in a periodic potential.

Quenching processes and premixed turbulent combustion diagrams

Abstract: The structure of premixed turbulent flames is a problem of fundamental interest in combustion theory. Possible flame geometries have been imagined and diagrams indicating the corresponding regimes of combustion have been constructed on the basis of essentially intuitive and dimensional considerations. A new approach to this problem is described in the present paper. An extended definition of flamelet regimes based on the existence of a continuous active (not quenched) flame front separating fresh gases and burnt products is first introduced. Direct numerical simulations of flame/vortex interactions using the full Navier–Stokes equations and a simplified chemistry model are then performed to predict flame quenching by isolated vortices. The formulation includes non-unity Lewis number, non-constant viscosity and heat losses so that the effect of stretch, curvature, transient dynamics and viscous dissipation can be accounted for. As a result, flame quenching by vortices (which is one of the key processes in premixed turbulent combustion) may be computed accurately. The effects of curvature and viscous dissipation on flame/vortex interactions may also be characterized by the same simulations. The influence of non-unity Lewis number and of thermo-diffusive processes in turbulent premixed combustion is discussed by comparing flame responses for two values of the Lewis number (Le = 0.8 and 1.2). An elementary (‘spectral’) diagram giving the response of one flame to a vortex pair is constructed. This spectral diagram is then used, along with certain assumptions, to establish a turbulent combustion diagram similar to those proposed by Borghi (1985) or Williams (1985). Results show that flame fronts are much more resistant to quenching by vortices than expected from the classical theories. A cut-off scale and a quenching scale are also obtained and compared with the characteristic scales proposed by Peters (1986). Results show that strain is not the only important parameters determining flame/vortex interaction. Heat losses, curvature, viscous dissipation and transient dynamics have significant effects, especially for small scales and they strongly influence the boundaries of the combustion regimes. It is found, for example, that the Klimov–Williams criterion which is generally advocated to limit the flamelet region, underestimates the size of this region by more than an order of magnitude.

Experimental study of turbulent swirling flow in a straight pipe.

Abstract: Swirling flow through a pipe is a highly complex turbulent flow and is still challenging to predict. An experimental investigation is performed to obtain systematic data about the flow and to understand its physics. A free-vortex-type swirling flow is introduced in a long straight circular pipe. The swirling component decays downstream as a result of wall friction. The velocity distributions are continuously changing as they approach fully developed parallel flow. The swirl intensity Ω, defined as a non-dimensional angular momentum flux, decays exponentially. The decay coefficients, however, are not constant as conventionally assumed, but depend on the swirl intensity. The wall shear stresses are measured by a direct method and, except in a short inlet region, are a function only of the swirl intensity and the Reynolds number. The velocity distributions and all Reynolds stress components are measured at various axial positions in the pipe. The structure of the tangential velocity profile is classified into three regions: core, annular and wall regions. The core region is characterized by a forced vortex motion and the flow is dependent upon the upstream conditions. In the annular region, the skewness of the velocity vector is noticeable and highly anisotropic so that the turbulent viscosity model does not work well here. The tangential velocity is expressed as a sum of free and forced vortex motion. In the wall region the skewness of the flow becomes weak, and the wall law modified by the Monin–Oboukhov formula is applicable. Data on the microscale and the spectrum are also presented and show quite different turbulence structures in the core and the outer regions.

Transient eddy formation around headlands

Abstract: Eddies with length scales of 1–10 km are commonly observed in coastal waters and play an important role in the dispersion of water-borne materials. The generation and evolution of these eddies by oscillatory tidal flow around coastal headlands is investigated with analytical and numerical models. Using shallow water depth-averaged vorticity dynamics, eddies are shown to form when flow separation occurs near the tip of the headland, causing intense vorticity generated along the headland to be injected into the interior. An analytic boundary layer model demonstrates that flow separation occurs when the pressure gradient along the boundary switches from favoring (accelerating) to adverse (decelerating), and its occurrence depends principally on three parameters: the aspect ratio [b/a], where b and a are characteristic width and length scales of the headland; [H/CDa], where H is the water depth, CD is the depth-averaged drag coefficient; and [Uo/σa], where Uo and σ are the magnitude and frequency of the far-field tidal flow. Simulations with a depth-averaged numerical model show a wide range of responses to changes in these parameters, including cases where no separation occurs, cases where only one eddy exists at a given time, and cases where bottom friction is weak enough that eddies produced during successive tidal cycles coexist, interacting strongly with each other. These simulations also demonstrate that in unsteady flow, a strong start-up vortex forms after the flow separates, leading to a much more intense patch of vorticity and stronger recirculation than found in steady flow.

On the dynamics of near-wall turbulence

Abstract: A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of `kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow

Mutual friction in superfluid 3He: Effects of bound states in the vortex core.

Abstract: The motion of singular quantized vortex lines in superfluid $^{3}\mathrm{He}$ is considered for the A and B phases. Mutual friction is calculated within a microscopic quantum-mechanical Green's-function formalism, valid for dynamical processes. This enables us to include all the different physical phenomena in a unified approach. We consider axisymmetric vortices for temperatures considerably lower than ${\mathit{T}}_{\mathit{c}}$. In this regime, the main contribution to the force exerted on a moving vortex originates from the localized Fermi excitations occupying quantized energy eigenstates in the vortex core. These $^{3}\mathrm{He}$ quasiparticle states are similar to the quantized motion of charge in a magnetic field; thus vortex motion in $^{3}\mathrm{He}$ resembles the Hall phenomenon in metals. The outcome is that the viscous drag cannot simply be expressed through the cross sections for $^{3}\mathrm{He}$ quasiparticles scattering off the vortex, but is rather due to the mutual interactions between the localized quasiparticles and the normal excitations. Our calculations conform with the experimental values for the mutual-friction parameters. We also discuss vortex oscillations, and predict that strong dissipation should be observed at a resonant frequency of about 10 kHz, owing to transitions between the bound-state energy levels. This effect could be used for detecting and measuring the quantization of the bound-state spectrum for superfluid $^{3}\mathrm{He}$ in the vortex-core matter.

Low-frequency pressure oscillations in a model ramjet combustor

Abstract: Low-frequency combustion instabilities are studied in a model ramjet combustor facility. The facility is two-dimensional, and is comprised of a long inlet duct, a dump combustor cavity with variable size capability, and an exhaust nozzle. The flame is observed to be unstable over a wide range of operating conditions. Acoustic pressure and velocity measurements are made at various locations in the system. They show that the inlet duct acts as a long-wavelength acoustic resonator. However, the instability frequency does not lock to any particular value. This result suggests that the instability mechanism is not purely acoustic in nature. Schlieren imaging reveals that the instability is associated with large-scale flame-front motions which are driven by periodic vortex shedding at the instability frequency. Vortices are generated at the dump in phase with the acoustic velocity fluctuations in the inlet duct. The unsteady heat addition process closely follows the vortex history: the vortices form, grow in size, convect through the combustor cavity, impinge on the exhaust nozzle, break down to small scales and burn. C2 and CH radical spectroscopy is used to determine the phase relation between heat release and pressure in the reaction zone. Rayleigh's criterion is thereby shown to be satisfied. Next, the crucial question of how the oscillation frequency is determined is addressed. Inlet velocity and combustor length are systematically varied to assess the role of vortices by modification of their characteristic lifetime. The influence of the acoustic feedback time is also studied by shortening the inlet duct. The results show that the instability frequency is controlled by both vortex kinetics in the combustor and acoustic response of the inlet section. Therefore, the instability may be considered as a mixed acoustic-convective mode. Finally, combining Rayleigh's criterion with a global feedback loop equation, it is found that the resonant frequencies are selected according to the restriction \[ \frac{1}{4N-1} < \frac{\tau_{\rm v}}{\tau_{\rm f}} < \frac{3}{4N-3}, \] where N is the mode of oscillation and τv is the time for vortices to be convected from inlet to exhaust with τf being the feedback time taken for a pressure disturbance to travel up the inlet system and back.

Thermal fluctuations and phase transitions in the vortex state of a layered superconductor.

Abstract: We study thermal fluctuations in a layered superconductor in the presence of a magnetic field applied orthogonal to the layers. A phase diagram for this case is proposed. In the weak-field region, fluctuations of a vortex lattice are of three-dimensional (3D) nature. This leads to a two-stage melting: When the temperature is raised, a phase transition to the vortex-line liquid occurs, then independent liquid systems of 2D vortices in different layers are formed. For fields larger than the crossover value, both fluctuations and melting of the vortex lattice become of 2D type. We study the effect of vortex-lattice fluctuations on the long-range superconducting order. We demonstrate the existence of a phase transition within the vortex-lattice state: The superconducting coherence between distant layers vanishes at a temperature which is substantially lower than the melting temperature.

Self-consistent electronic structure of a vortex line in a type-II superconductor.

Abstract: The electronic structure of a vortex line in a type-II superconductor is calculated self-consistently in the framework of the Bogoliubov--de Gennes theory. The Debye frequency, the Fermi velocity, and the coupling constant of the electron-electron attractive interaction are used as microscopic input parameters. The resulting quasiparticle-excitation spectrum, the pair potential, and the current distribution are studied as a function of temperature, and can be used to define a coherence length and to determine the magnetic penetration depth. The local density of one-particle excitations, calculated from the quasiparticle amplitudes, explains the results of scanning-tunneling-microscopy (STM) experiments by Hess et al. [Phys. Rev. Lett. 62, 214 (1989)] on ${\mathrm{NbSe}}_{2}$. The main spectroscopic features in the experimental results are caused by bound states in the vortex cores. Spatial distortions of the bound-state wave functions caused by neighboring vortices and by the crystalline lattice are discussed in terms of a simplified two-band model. In the case of ${\mathrm{NbSe}}_{2}$, the resulting local density of states has a characteristic star shape in real space, whose orientation is energy dependent, in agreement with recent STM experiments [Phys. Rev. Lett. 64, 2711 (1990)].

An experimental study of unstable barotropic vortices in a rotating fluid

Abstract: Laboratory experiments on barotropic vortices in a rotating fluid revealed that the instability behaviour of cyclonic and anticyclonic vortices is remarkably different. Depending on its initial vorticity distribution, the cyclonic vortex has in a number of experiments been observed to be unstable to wavenumber-2 perturbations, leading to the gradual formation of a stable tripolar vortex structure. This tripole consists of an elongated cyclonic core vortex adjoined by two anticyclonic satellite vortices.In contrast, the anticyclonic vortex shows a rather explosive instability behaviour, in the sense that it is observed to immediately split up into two dipoles. Under somewhat different circumstances the higher-order mode-3 instability is observed, in which the anticyclonic core has a triangular shape, with three smaller cyclonic satellite vortices at its sides.A modified version of Rayleigh's instability criterion offers a qualitative explanation for this apparent difference between unstable cyclonic and anticyclonic vortices.

SQUID picovoltometry of YBa2Cu3O7 single crystals: Evidence for a finite-temperature phase transition in the high-field vortex state.

Abstract: Using a SQUID picovoltmeter. we have measured current-voltage curves of YBa2Cu3O7 microtwinned crystals as a function of temperature in fields from I to 6 T. The data constitute evidence for a finite-temperature phase transition in the vortex state. Exponents derived within the framework of the vortex-glass model are found to be similar to thin-film values. Strongly temperature-dependent correlations in-volving up to 105 vortices near the transition. combined with the qualitative failure of thermal-activation models to fit our data. support the existence of a phase transition.

Tip Leakage Flow in Axial Compressors

Abstract: Experimental measurements in a linear cascade with tip clearance are complemented by numerical solutions of the three-dimensional Navier–Stokes equations in an investigation of tip leakage flow. Measurements reveal that the clearance flow, which separates near the entry of the tip gap, remains unattached for the majority of the blade chord when the tip clearance is similar to that typical of a machine. The numerical predictions of leakage flow rate agree very well with measurements, and detailed comparisons show that the mechanism of tip leakage is primarily inviscid. It is demonstrated by simple calculation that it is the static pressure field near the end of the blade that controls chordwise distribution of the flow across the tip. Although the presence of a vortex caused by the roll-up of the leakage flow may affect the local pressure field, the overall magnitude of the tip leakage flow remains strongly related to the aerodynamic loading of the blades.

Streamwise vortex production by pitched and skewed jets in a turbulent boundary layer

Abstract: Weak longitudinal (streamwise) vortices produced by the interaction of simple, round wall jets with a two-dimensional flow comprising a turbulent boundary layer were studied experimentally. Like the jets used in the vortex generator jet (VGJ) method of stall control, the jets were pitched up at 45 deg and skewed relative to the freestream as they entered from the wall.

Linear and nonlinear dust drift waves

Abstract: The linear and nonlinear properties of low-frequency motion in inhomogeneous, magnetized, dusty plasmas are investigated. The dynamics of the dust grains are taken into account by means of a fluid model. A new type of low-frequency waves, the dust-drift waves, is shown to exist. The nonlinear mode coupling equations are derived, and the possibility of propagating vortex structures is discussed. The dust-drift waves may be relevant in astrophysical and cometary plasmas.

Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems: Vortex cloud modelling by the boundary integral method

Abstract: Part I. The Surface Vorticity Boundary Integral Method of Fluid Flow Analysis: 1. The basis of surface singularity modelling 2. Lifting bodies, two-dimensional aerofoils and cascades 3. Mixed-flow and radial cascades 4. Bodies of revolution, ducts and annuli 5. Ducted propellers and fans 6. Three-dimensional and meridional flows in turbo-machines 7. Free vorticity shear layers and inverse methods Part II. Vortex Dynamics and Vortex Cloud Analysis: 8. Vortex dynamics in inviscid flows 9. Simulation of viscous diffusion in discrete vortex modelling 10. Vortex cloud modelling by the boundary integral method 11. Further development and applications of vortex cloud modelling to lifting bodies and cascades 12. Use of grid systems in vortex dynamics and meridional flows Appendix.

Review : vortex shedding lock-on and flow control in bluff body wakes

Abstract: The results of recent experiments demonstrate that the phenomenon of vortex shedding resonance or lock-on is observed also when a bluff body is placed in an incident mean flow with a periodic component superimposed upon it. This form of vortex shedding and lock-on exhibits a particularly strong resonance between the flow perturbations and the vortices, and provides one of several promising means for modification and control of the basic formulation and stability mechanisms in the near-wake of a bluff body. Examples are given of recent direct numerical simulations of the vortex lock-on in the periodic flow. These agree well with the results of experiments. A discussion also is given of vortex lock-on due to body oscillations both normal to and in-line with the incident mean flow, rotational oscillations of the body, and of the effect of sound on lock-on. The lock-on phenomenon is discussed in the overall context of active and passive wake control, on the basis of these and other recent and related results, with particular emphasis placed on active control of the circular cylinder wake.

On strongly nonlinear vortex/wave interactions in boundary-layer transition

Abstract: The interactions between longitudinal vortices and accompanying waves considered are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh wave nonlinear interactions are considered for the compressible boundary-layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. The strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.

Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems

Abstract: Part I. The Surface Vorticity Boundary Integral Method of Fluid Flow Analysis: 1. The basis of surface singularity modelling 2. Lifting bodies, two-dimensional aerofoils and cascades 3. Mixed-flow and radial cascades 4. Bodies of revolution, ducts and annuli 5. Ducted propellers and fans 6. Three-dimensional and meridional flows in turbo-machines 7. Free vorticity shear layers and inverse methods Part II. Vortex Dynamics and Vortex Cloud Analysis: 8. Vortex dynamics in inviscid flows 9. Simulation of viscous diffusion in discrete vortex modelling 10. Vortex cloud modelling by the boundary integral method 11. Further development and applications of vortex cloud modelling to lifting bodies and cascades 12. Use of grid systems in vortex dynamics and meridional flows Appendix.

Penetration of magnetic ac fields into type-II superconductors.

Abstract: The complex ac penetration depth, surface impedance, and susceptibility are calculated for a superconducting half space and film containing a vortex lattice of arbitrary orientation with respect to the surface. Within linear response theory, full account is taken of the correct boundary conditions (image vortices), diffuse driving force and nonlocal elasticity of the vortex lattice, collective and individual elastic pinning, flux flow (viscous drag), and thermally activated depinning (creep).

On the Goertler instability of boundary layers

Abstract: Abstract Gortler instability occurs due to the action of centrifugal forces in boundary layers over curved surfaces, where it most commonly results in the generation of steady streamwise vortices. This study provides a summary of the current knowledge of this phenomenon. All existing experimental evidence is discussed. Experimental facts that bear on the theoretical modelling of the instability are pointed out. Linear theory is discussed in details and compared critically with the available experiments. The nonlinear evolution of the vortices and their effect on the laminar-turbulent transition process are reviewed. The available nonlinear theories and direct numerical simulations are critically compared with the experiments. Centrifugal instability of turbulent boundary layers is discussed in detail. Effects of the instability on heat transfer and the associated buoyancy forces on the instability are discussed. A summary of some outstanding questions is given.

Small‐scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence

Abstract: Small‐scale structures of the vorticity and passive scalar fields have been examined by means of direct numerical simulations of homogeneous isotropic turbulence with 963 grid points and Rλ≊60. Both statistical and visual techniques have been used to examine the structure of certain quantities from the evolution equations for enstrophy and the scalar gradient. Tubelike regions of intense enstrophy contain large positive and sometimes large negative enstrophy production, and mostly moderate‐valued energy dissipation regions surround these tubes. The most intense regions of the scalar gradient are dissociated from the vortex tubes, and occur as large flat sheets. Within these sheets the scalar gradient production is large, the energy dissipation is small, and in their vicinity only moderate‐valued sheetlike enstrophy regions exist. The statistical techniques show that although activity in these intense regions is strong, on a volume normalized basis, by far the largest contributions to the terms in the evolution equations, along with the energy dissipation, are from low‐level ‘‘background’’ activity.

Vortices and defect statistics in two-dimensional optical chaos.

Abstract: We present the first direct experimental evidence of topological defects in nonlinear optics. For increasing Fresnel numbers F, the two-dimensional field is characterized by an increasing number of topological defects, from a single vortex, up to a large number of vortices with zero net topological charge. At variance with linear scattering from a fixed phase plate, here the defect pattern evolves in time according to the nonlinear dynamics. We assign the scaling exponents for the mean number of defects, their mean separation, and the charge unbalance as functions of F, as well as the correlation time of the defect pattern.

The linear inviscid secondary instability of longitudinal vortex structures in boundary layers

Abstract: The inviscid instability of a longitudinal vortex structure within a steady boundary layer is investigated. The instability has wavelength comparable with the boundary-layer thickness so that a quasi-parallel approach to the instability problem can be justified. The generalisation of the Rayleigh equation to such a flow is obtained and solved for the case when the vortex structure is induced by curvature. Two distinct modes of instability are found; these modes correspond with experimental observations on the breakdown process for Gortler vortices.

The kinematics of turbulent boundary layer structure

Abstract: The long history of research into the internal structure of turbulent boundary layers has not provided a unified picture of the physics responsible for turbulence production and dissipation. The goals of the present research are to: (1) define the current state of boundary layer structure knowledge; and (2) utilize direct numerical simulation results to help close the unresolved issues identified in part A and to unify the fragmented knowledge of various coherent motions into a consistent kinematic model of boundary layer structure. The results of the current study show that all classes of coherent motion in the low Reynolds number turbulent boundary layer may be related to vortical structures, but that no single form of vortex is representative of the wide variety of vortical structures observed. In particular, ejection and sweep motions, as well as entrainment from the free-streem are shown to have strong spatial and temporal relationships with vortical structures. Disturbances of vortex size, location, and intensity show that quasi-streamwise vortices dominate the buffer region, while transverse vortices and vortical arches dominate the wake region. Both types of vortical structure are common in the log region. The interrelationships between the various structures and the population distributions of vortices are combined into a conceptual kinematic model for the boundary layer. Aspects of vortical structure dynamics are also postulated, based on time-sequence animations of the numerically simulated flow.