Three-dimensional instability of an elliptic Kirchhoff vortex

The instability of a Kirchhoff vortex [1–3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4–6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4–9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1988.     

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.     

Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity

A new type of vibrational lift force [1] acting on a spherical body oscillating in a viscous fluid near a rigid boundary is experimentally investigated. The interaction between the body and the cavity boundary creates a repulsion force which is capable of holding a heavy body in the gravity field at a certain distance from the floor and a light body at a certain distance from the ceiling. The repulsion force appears at a distance comparable with the Stokesian boundary layer thickness and increases as the surface is approached. Outside the viscous interaction range, the repulsion force is replaced by an attraction force which decays with distance. Dimensionless parameters governing the vibrational interaction are found and threshold curves, corresponding to the transition of bodies of different densities to the “suspended” state, are plotted as functions of a dimensionless frequency. The dependence of the repulsion and attraction forces on the distance between the body and the wall is studied.     

Long-wave instability of a vortex ring

The instability of barrel-shaped vibrations of a vortex ring in an ideal fluid is investigated. These vibrations, stable for a vortex ring with a piecewise-uniform vorticity profile, appear to be unstable for a vortex ring with a smooth vorticity profile. The instability growth rate is found on the basis of the energy balance equation determining the energy transport from perturbations with negative energy in the critical layer to perturbations with positive energy in the rest of the flow. The curvature of the vortex ring, by virtue of which the perturbations with energies of different signs appear to be connected, plays a prominent role in the mechanism under consideration.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–78, November–December, 1995.     

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).     

Role of shear-thinning and viscoelasticity on the onset of instability of glass fiber suspensions in the concentric spherical gap between an inner rotating hemisphere and an outer stationary sphere

An experimental study investigated the effects of glass fiber suspensions on the onset of instability in the non-Newtonian fluid flow in the concentric spherical gaps between an inner rotating hemisphere and an outer stationary whole sphere. Glass fibers with different aspect ratios were mixed with a macromolecule polymeric solution to obtain different suspension fluids. For comparison, the pure macromolecule polymeric fluid was also investigated. The torques on the inner sphere were measured for various spherical gaps and various rotational Reynolds numbers. The onset of instability of the polymeric fluid flows was delayed by adding glass fibers to the polymeric solution for all tested gap ratios.     

Three-dimensional vortex formation on a heaving low-aspect-ratio wing: Computations and experiments

This paper addresses by means of high-resolution numerical simulations and experimental quantitative imaging the three-dimensional unsteady separation process induced by large-amplitude heaving oscillations of a low-aspect-ratio wing under low-Reynolds-number conditions. Computed results are found to be in good agreement with experimental flow visualizations and PIV measurements on selected cross-flow planes. The complex unsteady three-dimensional flow structure generated during dynamic stall of the low-aspect-ratio wing is elucidated. The process is characterized by the generation of a leading-edge vortex system which is pinned at the front corners of the plate and which exhibits intense transverse flow toward the wing centerline during its initial stages of development. This vortex detaches from the corners and evolves into an newly found arch-type structure. The legs of the arch vortex move along the surface toward the wing centerline and reconnect forming a ring-like structure which is shed as the next plunging cycle begins. Vortex breakdown, total collapse and reformation of the wing tip vortices are also observed at various stages of the heaving motion. At the relatively high value of reduced frequency considered, these basic flow elements of the complex three-dimensional dynamic stall process are found to persist over a range of Reynolds numbers.     

On the linear instability of the Hall-Stewartson vortex

It is demonstrated that the Hall-Stewartson leading-edge vortex is linearly unstable to viscous perturbations of the center-mode type. Center modes are found to occur in two reigons of Reynolds-number-wave-number space, in limits in which the axial wave number is large. The appropriate center-mode equations in these neighborhoods are established, and it emerges that the two sets are identical. The single system of equations, which depends on the azimuthal wave number m and a distance parameter only, is solved numerically for various values of m and . Highly unstable modes are found for large positive , and the results are shown to be in good agreement with proposed asymptotic expansions when >1. To lowest order, unstable modes have phase surfaces that rotate with the fluid: in addition constant phase surfaces propagate upstream but the group velocity is directed downstream. The growth rate of the instability increases faster than Reynolds number to the quarter power. This, together with the finding that the length scale of the unstable modes found goes to zero as the Reynolds number tends to infinity, makes this instability an unusual one.This work was supported by the Air Force Office of Scientific Research under contract AFOSR-89-0346 monitored by Dr. L. Sakell, and by the U.S. Army Research Office at the Mathematical Sciences Institute of Cornell University.     

Three-dimensional numerical simulation of a vortex ring impacting a bump

A vortex ring impinging on a three-dimensional bump is studied using large eddy simulation for a Reynolds number Re = 4 × 10⁴ based on the initial translation speed and diameter of the vortex ring. The effects of bump height on the vortical flow phenomena and the underlying physical mechanisms are investigated. Based on the analysis of the evolution of vortical structures, two typical kinds of vortical structures, i.e., the wrapping vortices and the hair-pin vortices, are identified and play an important role in the flow state evolution. The circulation of the primary vortex ring reasonably elucidates some typical phases of flow evolution. Furthermore, the mechanism of flow transition from laminar to turbulent state has been revealed based on analysis of turbulent kinetic energy.     

On the problem of vortex interaction with a plane

We consider the well-known problem of the interaction of a vortex filament with a perpendicular plane in a viscous incompressible fluid. In this study, the vortex filament is represented by a semi-infinite rotating needle. Different models are considered: a zero-radius needle and fixed and movable in the axial direction needles of a finite radius. The ranges of the existence of the solution are found, and the correspondence of the flow around a finite-radius needle to that around a zero-radius needle, as the needle radius decreases, is studied.     

From generation to chaotic motion of a ring configuration of vortex structures on a sphere

This is a review article of recent research developments on the motion of a polygonal ring configuration of vortex structures with singular vorticity distributions in incompressible and inviscid flows on a non-rotating sphere. Numerical computation of a single vortex sheet reveals that the Kelvin-Helmholtz instability gives rise to the formation of a polygonal ring arrangement of rolling-up spirals. An application of methods of Hamiltonian dynamics to the N-vortex problem on the sphere shows that the motion of the ring configuration of homogeneous point vortices, which is a simple model for the rolling-up spirals, becomes chaotic after a long time evolution. Some remarks on an extension of the present research and a generic non-self-similar collapse are also provided.     

Experiments on jet/vortex interaction

An experimental study was performed to evaluate the effect of a cold jet on a single trailing vortex. Flow visualization and particle image velocimetry (PIV) measurements were conducted in wind and water tunnels. The main parameters were the ratio of jet-to-vortex strength, the jet-to-vortex distance, the jet inclination angle and the Reynolds number. It was shown that the jet turbulence is wrapped around the vortex and ingested into it. This takes place faster with decreasing jet-to-vortex distance and increasing jet strength. Both time-averaged and instantaneous flow fields showed that the trailing vortex became diffused with its rotational velocity and vorticity levels reduced when the jet is located close to the vortex. The mechanism with which the jet interacts with the vortex is a combination of vortices shed by the jet and the turbulence. No noticeable differences were found within the Reynolds number range tested. The effect of jet on the vortex is delayed when the jet is blowing at an angle to the free stream and away from the vortex such as during take-off.