Showing papers on "Vortex published in 1982"

An Album of Fluid Motion

Abstract: Keywords: visualisation de l'ecoulement ; tourbillon ; dynamique des : fluides ; aubes ; cylindre ; instabilite ; ecoulement : secondaire Note: moult photos Reference Record created on 2005-11-18, modified on 2016-08-08

Subharmonics and vortex merging in mixing layers

Abstract: In the present study, it is shown that the spreading rate of a mixing layer can be greatly manipulated at very low forcing level if the mixing layer is perturbed near a subharmonic of the most-amplified frequency. The subharmonic forcing technique is able to make several vortices merge simultaneously and hence increases the spreading rate dramatically. A new mechanism, ‘collective interaction’, was found which can bypass the sequential stages of vortex merging and make a large number of vortices (ten or more) coalesce.A deeper physical insight into the evolution of the coherent structures is revealed through the investigation of a forced mixing layer. The stability and the forcing function play important roles in determining the initial formation of the vortices. The subharmonic starts to amplify at the location where the phase speed of the subharmonic matches that of the fundamental. The position where vortices are seen to align vertically coincides with the position where the measured subharmonic reaches its peak. This location is defined as the merging location, and it can be determined from the feedback equation (Ho & Nosseir 1981).The spreading rate and the velocity profiles of the forced mixing layer are distinctly different from the unforced case. The data show that the initial condition has a longlasting effect on the development of the mixing layer.

Strained spiral vortex model for turbulent fine structure

Abstract: A model for the intermittent fine structure of high Reynolds number turbulence is proposed. The model consists of slender axially strained spiral vortex solutions of the Navier–Stokes equation. The tightening of the spiral turns by the differential rotation of the induced swirling velocity produces a cascade of velocity fluctuations to smaller scale. The Kolmogorov energy spectrum is a result of this model.

The Response of Balanced Hurricanes to Local Sources of Heat and Momentum

Abstract: Eliassen's (1951) diagnostic technique is used to calculate the secondary circulation induced by point sources of heat and momentum in balanced, hurricane-like vortices. Scale analysis reveals that such responses are independent of the horizontal scale of the vortex. Analytic solutions for the secondary circulation are readily obtained in idealized barotropic vortices, but numerical methods are required for more realistic barotropic and baroclinic vortices. For sources near the radius of maximum wind, the local, two-dimensional, streamfunction dipole response of Eliassen is modified by both the spatial variations of the vortex structure and the influences of boundary conditions. The secondary flow advects mean-flow buoyancy and angular momentum and thus leads to a slow evolution of the vortex structure. In weak systems (maximum tangential wind <35 m s−1), the restraining influences of structure and boundaries lengthen the time scale of the vortex evolution. In stronger vortices, the horizontal sc...

Concentric Eye Walls, Secondary Wind Maxima, and The Evolution of the Hurricane vortex

Abstract: Research aircraft observations in recent hurricanes support the model of Shapiro and Willoughby (1982) for the tropical cyclone's response to circularly symmetric, convective heat sources (convective rings). In both nature and the numerical model the tangential wind commonly increases rapidly just inside the radius of maximum wind and decreases inside the eye near the central axis of the vortex. Thus both secondary outer wind maxima and eyewall wind maxima often contract as they intensify. This response is independent of the horizontal spatial scale of the maximum. An outer maximum is frequently observed to constrict about a pre-existing eye and replace it. This chain of events often coincides with a weakening, or at least a pause in intensification, of the vortex as a whole. The concentric eye phenomenon is a common, but by no means universal, feature of tropical cyclones. It is most frequently observed in intense, highly symmetric systems.

The two- and three-dimensional instabilities of a spatially periodic shear layer

Abstract: The two- and three-dimensional stability properties of the family of coherent shear-layer vortices discovered by Stuart are investigated. The stability problem is formulated as a non-separable eigenvalue problem in two independent variables, and solved numerically using spectral methods. It is found that there are two main classes of instabilities. The first class is subharmonic, and corresponds to pairing or localized pairing of vortex tubes; the pairing instability is most unstable in the two-dimensional limit, in which the perturbation has no spanwise variations. The second class repeats in the streamwise direction with the same periodicity as the basic flow. This mode is most unstable for spanwise wavelengths approximately 2/3 of the space between vortex centres, and can lead to the generation of streamwise vorticity and coherent ridges of upwelling. Comparison is made between the calculated instabilities and the observed pairing, helical pairing, and streak transitions. The theoretical and experimental results are found to be in reasonable agreement.

Turbulence and waves in a rotating tank

Abstract: A turbulent field is produced with an oscillating grid in a deep, rotating tank. Near the grid, the Rossby number is kept large, 0(3-33), and the turbulence is locally unaffected by rotation. Away from the grid, the scale of the turbulence increases, the r.m.s. turbulent velocity decreases, and rotation becomes increasingly important. The flow field changes dramatically at a local Rossby number of about 0.20, and thereafter remains independent of depth. The flow consists of concentrated vortices having axes approximately parallel to the rotation axis, and extending throughout the depth of the fluid above the turbulent Ekman layer. The number of vortices per unit area is a function of the grid Rossby number. The local vorticity within cores can be a factor of 50 larger than the tank vorticity 2Ω. The total relative circulation contained in the vortices remains, however, a small fraction of the tank circulation.The concentrated vortex cores support waves consisting of helical distortions, which travel along the axes of individual vortices. Isolated, travelling waves seem well-described by the vortex-soliton theory of Hasimoto (1972). The nonlinear waves transport mass, momentum and energy from the vigorously turbulent region near the grid to the rotation-dominated flow above. Interactions between waves, which are frequent occurrences, almost always result in a local breakdown of the vortex core, and small-scale turbulence production. Usually the portions of broken core reform within ½−1 rotation periods, but occasionally cores are destroyed and reformed on a much longer timescale.

Generalized vortex methods for free-surface flow problems

Abstract: The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source strengths. The resulting Fredholm integral equations of the second kind may be solved efficiently in both storage and work by iteration in both two and three dimensions. Applications to breaking water waves over finite-bottom topography and interacting triads of surface and interfacial waves are given.

Inertial Stability and Tropical Cyclone Development

Abstract: We consider the frictionless, axisymmetric, balanced flow occurring in a thermally forced vortex on an f-plane. Following Eliassen (1952) we derive the diagnostic equation for the forced secondary circulation. This equation contains the spatially varying coefficients A (static stability), B (baroclinity), C (inertial stability), and the thermal forcing Q. Assuming that A is a constant, B = 0, and that C and Q are piecewise constant functions of radius, we obtain analytical solutions for the forced secondary circulation. The solutions illustrate the following points. 1) For a given Q an increase in inertial stability leads to a decrease in the forced secondary circulation and a change in the radial distribution of local temperature change, with enhanced ∂θ/∂t; in the region of high inertial stability. 2) Lower tropospheric tangential wind accelerations are larger inside the radius of maximum wind, which leads to a collapse of the radius of maximum wind. 3) The fraction of Q which ends up as ∂θ/∂t;...

An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders

Abstract: Measurements are presented of the pressure fluctuations acting on a stationary squaresection cylinder, with the front face normal to the flow, and one forced to oscillate, transverse to a flow, at amplitudes up to 25% of the length of a side. The range of reduced velocities investigated, 4–13, includes the vortex lock-in regime. At lock-in the amplification of the coefficient of fluctuating lift is found to be much less than that found for a circular cylinder. The variation of the phase angle, between lift and displacement, is also different from that measured on a circular cylinder, and vortex-induced oscillations are possible only at the high-reduced-velocity end of the lock-in range. At reduced velocities sufficiently far below lock-in the natural vortex-shedding mode is suppressed and vortices are found to form over the side faces at the body frequency. Intermittent reattachment occurs over the side faces and, for an amplitude of oscillation equal to 10% of the length of a side face, the time-mean drag coefficient can be reduced to 60% of its fixed-cylinder value.

A numerical study of vortex shedding from rectangles

Abstract: The purpose of this paper is to present numerical solutions for two-dimensional time-dependent flow about rectangles in infinite domains. The numerical method utilizes third-order upwind differencing for convection and a Leith type of temporal differencing. An attempted use of a lower-order scheme and its inadequacies are also described. The Reynolds-number regime investigated is from 100 to 2800. Other parameters that are varied are upstream velocity profile, angle of attack, and rectangle dimensions. The initiation and subsequent development of the vortex-shedding phenomenon is investigated. Passive marker particles provide an exceptional visualization of the evolution of the vortices both during and after they are shed. The properties of these vortices are found to be strongly dependent on Reynolds number, as are lift, drag, and Strouhal number. Computed Strouhal numbers compare well with those obtained from a wind-tunnel test for Reynolds numbers below 1000.

Vortex methods. II. Higher order accuracy in two and three dimensions

Abstract: In an earlier paper the authors introduced a new version of the vortex method for three-dimensional, incompressible flows and proved that it converges to arbitrarily high order accuracy, provided we assume the consistency of a discrete approximation to the Biot-Savart Law. We prove this consistency statement here, and also derive substantially sharper results for two-dimensional flows. A complete, simplified proof of convergence in two dimensions is included.

Motions in a Bose condensate. IV. Axisymmetric solitary waves

Abstract: Axisymmetric disturbances that preserve their form as they move through a Bose condensate are obtained numerically by the solution of the appropriate nonlinear Schrodinger equation. A continuous family is obtained that, in the momentum (p)-energy (E) plane, consists of two branches meeting at a cusp of minimum momentum around 0.140 PK~/C' and minimum energy about 0.145 p~~/c, where p is density, c is the speed of sound and K is the quantum of circulation. For all larger p, there are two possible energy states. One (the lower branch) is (for large enough p) a vortex ring of circulation K; as p+m its radius G-(~/TK)"* becomes infinite and its forward velocity tends to zero. The other (the upper branch) lacks vorticity and is a rarefaction sound pulse that becomes increasingly one dimensional as p +a; its velocity approaches c for large p. The velocity of any member of the family is shown, both numerically and analytically, to be aE/ap, the derivative being taken along the family. At great distances, the disturbance in the condensate is pseudo-dipolar (dipolar in a stretched coordinate system); the strength of the pseudo-dipole moment is obtained numerically. Analogous calculations are presen- ted for the corresponding two-dimensional problem. Again, a continuous sequence of solitary waves is obtained, but the momentum per unit length p and energy per unit length E have no minima. For small forward velocities, the wave consists of two widely separated parallel, oppositely directed line vortices. As the forward velocity increases the wave loses its vorticity and becomes a rarefaction pulse of ever increasing spatial extent but ever decreasing amplitude. As its velocity approaches c, both p and E tend to zero, and Elp + c.

Vortex methods. I. Convergence in three dimensions

Abstract: Recently several different approaches have been developed for the simulation of three-dimensional incompressible fluid flows using vortex methods. Some versions use detailed tracking of vortex filament structures and often local curvatures of these filaments, while other methods require only crude information, such as the vortex blobs of the two-dimensional case. Can such "crude" algorithms accurately account for vortex stretching and converge? We answer this question affirmatively by constructing a new class of "crude" three-dimensional vortex methods and then proving that these methods are stable and convergent, and can even have arbitrarily high order accuracy without being more expensive than other "crude" versions of the vortex algorithm.

Taylor—Gortler vortices in fully developed or boundary-layer flows: linear theory

Abstract: The stability characteristics of some fluid flows at high Taylor or Gortler numbers are determined using perturbation methods. In particular, the stability characteristics of some fully developed flows between concentric cylinders driven either by a pressure gradient or the motion of the inner cylinder are investigated. The asymptotic structure of short-wavelength disturbances to these flows is obtained and used as a basis for a formal perturbation solution to the corresponding stability problem appropriate to a developing boundary layer. The non-parallel effect of the basic flow on the condition for neutral stability is discussed. The results obtained suggest that the disturbances are concentrated in internal viscous or critical layers well away from the wall and the free stream. The stability of a boundary layer on a concave wall to Gortler vortices that propagate downstream is also considered. These modes are found to be more stable than the usual time-independent modes and they propagate downstream with the speed of the basic flow in the critical layer. Some comparison with previous experimental and theoretical work is given.

Visualization studies of a shear driven three-dimensional recirculating flow

Abstract: A facility has been constructed to study shear-driven, recirculating flows. In this particular study, the circulation cell structure in the lid-driven cavity was studied as a function of the speed of the lid which provides the shearing force to a constant and uniform density fluid. The flow is three-dimensional and exhibits regions where Taylor-type instabilities and Taylor Goertler-like vortices are present. One main circulation cell and three secondary cells are present for the Reynolds number (based on cavity width and lid speed) range considered, viz., 1000-10000. The flows becomes turbulent at Reynolds numbers between 6000 to 8000. The transverse fluid motions (in the direction perpendicular to the lid motion) are significant. In spite of this, some key results from two-dimensional numerical simulations agree well with the results of the present cavity experiments.

Acoustic streaming in swirling flow and the Ranque—Hilsch (vortex-tube) effect

Abstract: The Ranque–Hilsch effect, observed in swirling flow within a single tube, is a spontaneous separation of total temperature, with the colder stream near the tube centreline and the hotter air near its periphery. Despite its simplicity, the mechanism of the Ranque–Hilsch effect has been a matter of long-standing dispute. Here we demonstrate, through analysis and experiment, that the acoustic streaming, induced by orderly disturbances within the swirling flow is, to a substantial degree, a cause of the Ranque–Hilsch effect. The analysis predicts that the streaming induced by the pure tone, a spinning wave corresponding to the first tangential mode, deforms the base Rankine vortex into a forced vortex, resulting in total temperature separation in the radial direction. This is confirmed by experiments, where, in the Ranque–Hilsch tube of uniflow arrangement, we install acoustic suppressors of organ-pipe type, tuned to the discrete frequency of the first tangential mode, attenuate its amplitude, and show that this does indeed reduce the total temperature separation.

The evolution of a turbulent vortex

Abstract: We examine numerically the evolution of a perturbed vortex in a periodic box. The fluid is inviscid. We find that the vorticity blows up. The support of theL2 norm of the vorticity converges to a set of Hausdorff dimension ∼2.5. The distribution of the vorticity seems to converge to a lognormal distribution. We do not observe a convergence of the higher statistics towards universal statistics, but do observe a strong temporal intermittency.

Dynamics of spin vortices in two-dimensional planar magnets

Abstract: We investigate the dynamics of a dilute gas of free spin vortices in a two-dimensional planar magnet. An equation of motion for the spin vortex is presented and compared with the corresponding equation for a vortex in a superfluid film. Exploiting a similar analogy with the dynamics of a two-dimensional plasma in a perpendicular magnetic field we calculate the mean-square vortex velocity and the vortex self-diffusion constant in the critical region above the phase transition. When combined with equations obtained previously for the spin-autocorrelation functions, our results provide an approximate description of the vortex contribution to the critical dynamics outside of the hydrodynamic regime.

Evolution and Merger of Isolated Vortex Structures.

Abstract: Numerical simulations of the instability, merger, and breaking of two piecewise‐constant finite‐area vortex regions (FAVR’s) are presented. An improved contour dynamical algorithm with node insertion‐and‐removal to maintain the a p r i o r i accuracy is used. Corotating ’’V states’’ (symmetric steady‐state FAVR’s) were found to be unstable when properly perturbed if their centroid‐effective radius ratio, x/R, is <1.6, thereby verifying an estimate of Saffman and Szeto. This causes the FAVR’s to approach at an exponential rate, merge, and reform into a stable perturbed elliptical structure with filamentary arms (to conserve angular momentum). For larger x/R ratios, regular perimeter oscillations were observed and estimates of an eigenfrequency of the perturbed stable V states were obtained. When regions of different vorticity density merge, the larger‐density region is eventually entrained within the smaller‐density region. These simulations elucidate the self‐consistent close interactions of isolated vortex regions in two‐dimensional high Reynolds number flows.

Self-sustained low-frequency components in an impinging shear layer

Abstract: Oscillations of a cavity shear layer, involving a downstream-travelling wave and associated vortex formation, its impingement upon the cavity corner, and upstream influence of this vortex-corner interaction are the subject of this experimental investigation.Spectral analysis of the downstream-travelling wave reveals low-frequency components having substantial amplitudes relative to that of the fundamental (instability) frequency component; using bicoherence analysis it is shown that the lowest-frequency component can interact with the fundamental either to reinforce itself or to produce an additional (weaker) low-frequency component. In both cases, all frequency components exhibit an overall phase difference of almost 2kπ(k = 1, 2,…) between separation and impingement. Furthermore, the low-frequency and fundamental components have approximately the same amplitude growth rates and phase speeds; this suggests that the instability wave is amplitude-modulated at the low frequency, as confirmed by the form of instantaneous velocity traces.At the downstream corner of the cavity, successive vortices, arising from the amplified instability wave, undergo organized variations in (transverse) impingement location, producing a low-frequency component(s) of corner pressure. The spectral content and instantaneous trace of this impingement pressure are consistent with those of velocity fluctuations near the (upstream) shear-layer separation edge, giving evidence of the strong upstream influence of the corner region.

Some Recent Studies of Vortex Shedding With Application to Marine Tubulars and Risers

Abstract: A discussion is given in this paper of the problems caused by vortex shedding from flexible, bluff cylinders in steady current flows. In particular, recent measurements of the steady and unsteady deflections caused by the vortex-excited drag and lift forces are discussed. 48 refs.

Mechanism of Instabilities in Turbulent Combustion Leading to Flashback

Abstract: High-speed schlieren cinematography, combined with synchronized pressure transducer records, was used to investigate the mechanism of combustion instabilities leading to flashback. The combustion chamber had an oblong rectangular cross-section to model the essential features of planar flow, and was provided with a rearward facing step acting as a flameholder. As the rich limit was approached, three instability modes were observed: (1) humming - a significant increase in the amplitude of the vortex pattern; (2) buzzing - a large-scale oscillation of the flame; and (3) chucking - a cyclic reformation of the flame, which results in flashback. The mechanism of these phenomena is ascribed to the action of vortices in the recirculation zone and their interactions with the trailing vortex pattern of the turbulent mixing layer behind the step.

The structure of the large eddies in fully developed turbulent shear flows. Part 2. The plane wake

Abstract: A set of measurements using arrays of hot-wire anemometers has been performed in the fully developed turbulent wake of a circular cylinder. The data were digitized, recorded on magnetic tape, and processed using the pattern recognition technique described in Part 1 (Mumford 1982), to yield ensemble averages of the streamwise component of the velocity fields of the large eddies in the flow.The results indicate that the large-scale structures in the turbulent wake are predominantly the inclined ‘double-roller’ vortices described by Grant (1958). These eddies consist of two contrarotating roller-like vortices with parallel axes displaced in the spanwise direction and approximately aligned with the direction of the strain associated with the mean velocity gradient. It was found that the structures are often confined to either side of the wake centreplane, rather than extending over the entire thickness of the turbulent region. In addition, eddies of similar type tended to occur in pairs or longer groups with their centres separated in the stream direction.

Multi-armed vortices in an active chemical medium

Abstract: An excellent example of self-organization in nonequilibrium systems1,2 is the origination of rotating spiral vortices. These vortices have been observed in a wide range of active media—in the morphogenesis processes of social amoeba Dictyostelium discoideum3,4, in cardiac muscle during some arrhythmias5 and in the Belousov–Zhabotinsky reaction6–9. All these vortices are simple spirals. The rotating structures of a higher order of symmetry such as multiarmed vortices have not previously been observed experimentally. We have obtained two-, three- and four-armed rotating spiral vortices in an active chemical medium. These structures were appreciably stable and we observed their rotation for more than half an hour, which was in striking contrast to unstable multiple vortices in many other physical systems (such as superfluid 4He or superconductors10,11).

Vortex-flow regimes

Abstract: Analysis of a considerable body of new data, based upon flow-visualization experiments, reveals a simple criterion for the occurrence of vortex breakdown at a fixed location in a tube: ReB ∼ Ω-3 R−1, where Ω is the circulation number, R the ratio of the radial to tangential velocities in the inflow region, and ReB the pipe Reynolds number at which vortex breakdown occurs. The constant of proportionality is found to be practically independent both of the pipe flare angle α and the type of breakdown observed (bubble, spiral, etc.) although the latter is shown to depend on ReB. Theoretical support for the experimental results is derived from the analysis of Benjamin (1962) combined with similarity arguments.

Laboratory experiments on fronts

Abstract: We describe a laboratory model of an upwelling front in a two-layer stratification. In the model the interface between the two layers slopes upwards toward a vertical boundary (or coastline) and can intersect the free surface to produce a front. Fluid motion in each layer is density driven and, in the undisturbed state, is in quasi-geostrophic balance. The front is observed to be unstable to (ageostrophic) disturbances with an along-front wavelength proportional to the Rossby radius of deformation. At very large amplitudes these unstable waves form closed circulations. However, in contrast to the behaviour of fronts far from vertical boundaries, where cyclone-anticyclone vortex pairs are formed, the presence of the coastline inhibits formation of anticyclonic eddies in the upper layer and enhances cyclonic rings of upper layer fluid which lie above cyclonic eddies in the lower layer. The cyclones move away from the vertical boundary and (as is also the case when no vertical boundary is present) t...

Discrete-vortex simulation of a turbulent separation bubble

Abstract: The discrete-vortex model is applied to simulate the separation bubble over a two- dimensional blunt flat plate with finite thickness and right-angled corners, which is aligned parallel to a uniform approaching stream. This flow situation is chosen because, unlike most previous applications of the model, the separation bubble is supposed to be strongly affected by a nearby solid surface. The major objective of this paper is to examine to what extent the discrete-vortex model is effective for such a flow. A simple procedure is employed to represent the effect of viscosity near the solid surface; in particular, the no-slip condition on the solid surface. A reduction in the circulation of elemental vortices is introduced as a function of their ages in order to represent the three-dimensional deformation of vortex filaments, An experiment was also performed for comparison purposes.The calculation yielded reasonable predictions of the time-mean and r.m.s. values of the velocity and the surface-pressure fluctuations, together with correlations between their fluctuating components, over most of the separation bubble. The interrelation between instantaneous spatial variations of the surface-pressure and velocity fluctuations were also obtained. A comparison between the calculated and measured results suggests that, in the real flow, the three-dimensional deformation of vortex filaments will become more and more dominant as the reattachment point is approached.