Characterising shortwave instabilities on a vortex dipole

The paper presents a method for characterising shortwave instability on a vortex dipole. Such instabilities cause the initially straight vortex lines to deform in a sinuous manner. In order to quantify the phenomenon, it is necessary to (a) characterise the vortex dipole and (b) characterise instabilities developed on it. In this study, the vortex dipole characteristics were quantified by using a nonlinear least squares fit to a Lamb–Oseen vortex profile with the velocity field measured by means of particle image velocimetry. The instability was recorded by capturing images of hydrogen bubbles, which were used to mark the vortex centre line, with a CCD camera. It was characterised by applying a fast Fourier transform and seeking dominant wavenumber components and a representative amplitude based on a range of wavenumbers within a bandwidth of interest. The method was tested on simulated and real data. Using the simulated data, the shortwave instability growth rate was calculated with an uncertainty of better than 1% and the mean wavelength deduced with an uncertainty of 5.3%. Using real data, a constant initial growth rate was deduced in agreement with the established theory. Further work might improve the algorithms so that spatial variations in wavelength and growth rate can be determined.     

Acoustic emission from interaction of a vortex ring with a sphere

Acoustic waves emitted by a vortex ring interacting with a fixed solid sphere are studied experimentally and theoretically. The experiments are carried out for two kindsof vortex-sphere arrangement: (A) a vortex ring passes over the sphere, and (B) a vortex ring passes by the sphere. The vortex motion is examined optically by means of a photosensor system, and the pressure signals of the emitted wave are detected by 1/2-inch microphones in the far field. In case A, the measured diameter of the vortex ring after passing the sphere increases from its initial diameter. The observed acoustic wave is dominated mainly by a dipole emission, and some contribution from a quadrupole radiation is present. In case B, the emitted wave is characterized by a rotating dipole emission in which the dipole axis rotates as the vortex position changes relative to the sphere.     

Singular vortices in regular flows

A review of the theory of quasigeostrophic singular vortices embedded in regular flows is presented with emphasis on recent results. The equations governing the joint evolution of singular vortices and regular flow, and the conservation laws (integrals) yielded by these equations are presented. Using these integrals, we prove the nonlinear stability of a vortex pair on the f-plane with respect to any small regular perturbation with finite energy and enstrophy. On the β-plane, a new exact steady-state solution is presented, a hybrid regular-singular modon comprised of a singular vortex and a localized regular component. The unsteady drift of an individual singular β-plane vortex confined to one layer of a two-layer fluid is considered. Analysis of the β-gyres shows that the vortex trajectory is similar to that of a barotropic monopole on the β-plane. Non-stationary behavior of a dipole interacting with a radial flow produced by a point source in a 2D fluid is examined. The dipole always survives after collision with the source and accelerates (decelerates) in a convergent (divergent) radial flow.     

Numerical study of vortex interactions behind two circular cylinders in bistable flow regime

A two-dimensional discrete-vortex model was used to investigate vortex interaction inside the near wakes of two circular cylinders in side-by-side arrangement within bistable flow regime. Two phases of vortex evolution are mainly identified in the near wakes: a symmetric shedding phase, characterized by two antiphase vortex streets, and a flip-flopping phase, characterized by biased gap flow, switching at irregular intervals. For the flip-flopping phase, vortex amalgamation, vortex pairing and dipole are found. Vortex dynamics of the flow is presented and its possible effects on the flow parameters are discussed. The initiation and transition from the symmetric to flip-flopping phase are caused by the asymmetry of one of the gap vortices. Flow visualization and quantitative results obtained seem to support the findings from the model.     

Numerical investigation of the interaction of a vortex dipole with a deformable plate

Energy harvesting from coherent fluid structures is a current research topic due to its application in the design of small self-powered sensors for underwater applications. The impact of a vortex dipole with a deformable cantilevered plate at the plate tip is herein studied numerically using a strongly coupled staggered fluid–structure interaction algorithm. Three dipole Reynolds numbers, Re=500, 1500, and 3000, are investigated for constant plate properties. As the dipole approaches the plate, positive vorticity is produced on the impact face, while negative vorticity is generated at the tip of the plate. Upon impact, the dipole splits into two, and two secondary dipoles are formed. The circulation and, therefore, the trajectories of these dipoles depend on both the Reynolds number and the elasticity of the plate, and these secondary dipoles may return for subsequent impacts. While the maximum deflection of the plate does not depend significantly on Reynolds number, the plate response due to subsequent impacts of secondary dipoles does vary with Reynolds number. These results elucidate the strong interdependency between plate deformation and vortex dynamics, as well as the effect of Reynolds number on both.     

INFLUENCE OF SEPARATION ON SOUND GENERATED BY VORTEX-STEP INTERACTION

An analysis of the sound produced when a line vortex interacts at low Mach number with forward or backward facing steps is made. The radiation is dominated by an aeroacoustic dipole whose strength is equal to the unsteady drag on the step. The drag is determined by the vorticity distribution, and a correct estimate of the sound must therefore include contributions from vorticity in the separated flow induced by the vortex. The separation is modelled by assuming that the shed vorticity rolls up into a concentrated core, fed by a connecting sheet from the edge of the step of negligible circulation. The motion everywhere is irrotational except at the impinging vortex and the separation core, and the trajectory of the core is governed by an emended Brown & Michael equation. For large steps it is found that estimates of the generated sound that neglect separation are typically an order of magnitude too large. The sound levels predicted for small steps with and without separation are of comparable magnitudes, although the respectivephasesare different.Turbulentflow over a step frequently involves separation and large surface pressure fluctuations at reattachment zones. The results of this paper suggest that numerical schemes for determining the noise generated by turbulent flow over a step must take proper account of “forcing” of the separation region by the impinging turbulence and of vorticity production via the no-slip condition.     

Acoustic waves emitted by a vortex ring passing near a wedge-like plate

Acoustic waves emitted by a vortex ring moving near a thin wedge-like plate of finite width have been studied. The experiments are performed for three configurations: the plate (A) is held edgeways to the direction of the vortex motion, (B) is held sideways to the direction, and (C) is held edgeways at an angle of 45° against the vortex motion. The observed sound wave is of dipole radiation type, and the magnitude of the pressure is large in the direction of the normal to the plate plane and small in parallel. The observed pressure is proportional to the third power of the vortex speed. The instantaneous force exerted on the plate by the vortex motion has also been examined. The force vector is mainly normal to the plate plane. The observed profiles agree within a reasonable degree of accuracy with the theoretical ones calculated for the vortex ring interacting with the flat plate of thickness zero.     

Coherent structures in unsteady swirling jet flow

An LDA technique and phase-averaging analysis were used to study unsteady precessing flow in a model vortex burner. Detailed measurements were made for Re=15,000 and S=1.01. On the basis of the analysis of phase-averaged data and vortex detection by the λ₂-technique of Joeng and Hussain (1995), three precessing spiral vortex structures were identified: primary vortex (PV), inner secondary vortex (ISV), and outer secondary vortex (OSV). The PV is the primary and most powerful structure as it includes primary vorticity generated by the swirler; the ISV and OSV are considered here as secondary vortical structures. The jet breakdown zone is the conjunction of a pair of co-rotating co-winding spiral vortices, PV and ISV. The interesting new feature described is that the secondary vortices form a three-dimensional vortex dipole with a helical geometry. The effect of coupling of secondary vortices was suggested as a mechanism of enhanced stability reflected in their increased axial extent.     

Mechanisms of wake deflection angle change behind a heaving airfoil

An immersed-boundary numerical method is applied to simulate the wake downstream of a two-dimensional heaving airfoil. A switch of vortex pattern is found to be the major reason that a deflected asymmetric wake reverses its deflection angle. Parameters of the heaving airfoil and flow that influence the onset and location of the vortex switching are discussed. While the previous literature deliberately discussed the wake deflection in the near wake region, this study shows that the deflection angle can change from the near wake to far wake regions. A cross-flow effective phase velocity is introduced to analyze the already-formed asymmetric wake behind the airfoil. A vortex dipole model and the related vortex dynamics analysis are developed to show that the change of the distance between the vortices is the primary factor that leads to the vortex pattern switching in the far wake.     

Motion of an intense vortex on a rotating globe

The evolution of an initially circular vortex is considered in terms of the relation between its dimensions and the screening scale — the radius of deformation of the quasigeostrophic single-layer model in the betaplane. It is shown that the beta-effect causes the displacement of the center of the vortex as a result of wave drift and secondary flows of dipole structure, whose development is analyzed asymptotically. It is found that with increase in the radius of deformation relative to the dimensions of the vortex the velocity of its center with respect to latitude becomes greater than the velocity with respect to longitude. The change in the intensity of the vortex due to the motion of its center with respect to latitude is estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 68–77, March–April, 1988.     

Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).     

Vortex Dipoles Impinging on Finite Aspect Ratio Rectangular Obstacles

Numerical simulations of a vortex dipole rebound from finite aspect ratio rectangular obstacles are presented. Compared to the dipole interaction with infinite flat walls studied by Orlandi (Phys. Fluids A2 (1990) 1429) new phenomena are observed. Secondary dipoles formed after the first rebound can undergo head-on collisions and partner exchange. A new lifting dipole is generated, moving in the opposite direction of the initial dipole. This phenomenon occurs for a ratio between the half-width of the obstacle and the dipole radius lower than a critical value depending on the Reynolds number of the flow. Scatter plots show a quasi-linear vorticity-stream function relationship for the lifting dipole. Some passive control strategies to inhibit the generation of lifting dipoles are also suggested.     

Numerical and experimental study of the interaction between a vortex dipole and a circular cylinder

This paper describes a study of the centred collision between a dipolar vortex and a solid circular cylinder. The flow was analysed experimentally by using dye visualizations and streak photography. Flow characteristics such as vorticity fields and the transport of passive tracers were compared with numerical simulations. Observations revealed that thin layers of vorticity, created at the cylinder wall are advected by the primary dipole halves, which, while rolling up into compact patches, give rise to the formation of two new asymmetric dipoles that move away along curved trajectories. The structure of the vorticity distribution inside the dipole, before and after the collision, has been investigated. Both the numerical and the experimental results indicate that the vorticity patches originating from the original primary dipole approximately preserve their original functional relationship =f(), while the secondary vorticity patches show a tendency to organize into structures attaining a similar relationship.One of us (JBF) gratefully acknowledges financial support by the Foundation for Fundamental Research on Matter (FOM) of the Netherlands Organization for Pure Research (NWO).     

Two-dimensional anisotropic vortex–bright soliton and its dynamics in dipolar Bose–Einstein condensates in optical lattice

We study construction and dynamics of two-dimensional (2D) anisotropic vortex–bright (VB) soliton in spinor dipolar Bose–Einstein condensates confined in a 2D optical lattice (OL), with two localized components linearly mixed by the spin–orbit coupling and long-range dipole–dipole interaction (DDI). It is found that the OL and DDI can support stable anisotropic VB soliton in the present setting for arbitrarily small value of norm N. We then present a new method via examining the mean square error of norm share of bright component to implement stability analysis. It is revealed that one can control the stability of anisotropic VB soliton only by adjusting OL depth for a fixed DDI. In addition, the dynamics of the anisotropic VB soliton was studied by applying the kick to them. The mobility of the single kicked VB soliton is Rabbi-like oscillation. However, for the collision dynamics of two kicked anisotropic VB solitons, their properties mainly depend on their initial distance and OL, and they can realize the transition from the bright component to the vortex component. Our work may provide a convenient way to prepare and manipulate anisotropic VB soliton in high-dimensional space.

     

Dipole-wall collision in a shallow fluid

Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow fluid layer have clearly shown the importance of vertical secondary flows on top of the primary horizontal motion. The present contribution focuses on the interaction of such a dipolar vortex with a sidewall. Accurate measurements of the three velocity components in a single horizontal plane have been performed using the Stereoscopic Particle Image Velocimetry (SPIV) technique. The experimental results, supported by numerical simulations, indicate that the complex vertical structure of a shallow-layer dipole becomes even more complex during the collision process. The observed growth of the kinetic energy associated with enhanced vertical motion pinpoints the strong discrepancies between vortex-wall interactions in shallow fluid layers and in purely two-dimensional wall-bounded turbulence.     

Self-sustained oscillations of a confined impinging jet

The present paper investigates the dynamics of a laminar plane jet impinging on a flat plate in a channel. An experimental parametric study is carried out to determine the flow regimes at different levels of confinement and Reynolds numbers. For very confined jets, the flow is steady whatever the Reynolds number. The overall structure of the flow is symmetric with respect to the jet axis and is characterized by the presence of recirculation zones at the channel walls. The dynamics is radically different for less confined jets. Above a critical Reynolds number, the flow bifurcates in the form of an oscillating flapping mode of the impinging jet. Analyses of the experimental results provide with a quantitative characterization of this regime in terms of amplitude, wavelength and frequency. This self-oscillating bifurcated flow induces strong sweepings of the target plate by the jet and intense vortex dipole ejections from the impacted wall. Such a regime is expected to be particularly useful in the enhancement of the local heat transfer at relatively low cost in terms of flow rate.     

Fast numerical evaluation of flow fields with vortex cells

A vortex cell (in this paper) is an aerodynamically shaped cavity in the surface of a body, for example a wing, designed specially to trap the separated vortex within it, thus preventing large-scale unsteady vortex shedding from the wing. Vortex stabilisation can be achieved either by the special geometry, as has already been done experimentally, or by a system of active control. In realistic conditions the boundary and mixing layers in the vortex cell are always turbulent. In the present study a model for calculating the flow in a vortex cell was obtained by replacing the laminar viscosity with the turbulent viscosity in the known high-Reynolds-number asymptotic theory of steady laminar flows in vortex cells. The model was implemented numerically and was shown to be faster than solving the Reynolds-averaged Navier–Stokes equations. An experimental facility with a vortex cell was built and experiments performed. Comparisons of the experimental results with the predictions of the model are reasonably satisfactory. The results also indicate that at least for flows in near-circular vortex cells it is sufficient to have accurate turbulence models only in thin viscous layers, while outside the viscosity should only be small enough to make the flow effectively inviscid.     

Research on the particle dispersion in the particulate two-phase round jet

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Numerical Simulation of the Evolution of Intensive Convective Vortices of the Typhoon Type in a Rotating Fluid

The problem of the generation of a vortex in a rotating vessel locally heated from below is considered. The results of calculating the regime of formation of an intense vortex from a large-scale advective cell are given. The spiral vortex obtained is characterized by cyclonic rotation at a velocity of an order of magnitude greater than the vessel's rate of rotation. The vortex has the characteristic features of atmospheric typhoons. A comparison of the results with the data of analogous laboratory experiments shows that they are in good agreement. The vortex flow restructuring stages after heating is interrupted are also investigated. It is shown that in this case the development of Rayleigh-Taylor instability favours for the formation of extended spiral branches.