Showing papers on "Starting vortex published in 2000"

Dynamics of vortex tangle without mutual friction in superfluid 4 He

Abstract: A recent experiment has shown that a tangle of quantized vortices in superfluid ${}^{4}\mathrm{He}$ decayed even at mK temperatures where the normal fluid was negligible and no mutual friction worked. Motivated by this experiment, this work studies numerically the dynamics of the vortex tangle without the mutual friction, thus showing that a self-similar cascade process, whereby large vortex loops break up to smaller ones, proceeds in the vortex tangle and is closely related with its free decay. This cascade process which may be covered with the mutual friction at higher temperatures is just the one at zero temperature Feynman proposed long ago. The full Biot-Savart calculation is made for dilute vortices, while the localized induction approximation is used for a dense tangle. The former finds the elementary scenario: the reconnection of the vortices excites vortex waves along them and makes them kinked, which could be suppressed if the mutual friction worked. The kinked parts reconnect with the vortex they belong to, dividing into small loops. The latter simulation under the localized induction approximation shows that such cascade process actually proceeds self-similarly in a dense tangle and continues to make small vortices. Considering that the vortices of the interatomic size no longer keep the picture of vortex, the cascade process leads to the decay of the vortex line density. The presence of the cascade process is supported also by investigating the classification of the reconnection type and the size distribution of vortices. The decay of the vortex line density is consistent with the solution of the Vinen's equation which was originally derived on the basis of the idea of homogeneous turbulence with the cascade process. The cascade process revealed by this work is an intrinsic process in the superfluid system free from the normal fluid. The obtained result is compared with the recent Vinen's theory which discusses the Kelvin wave cascade with sound radiation.

Heat Transfer and Fluid Flow in a Square Duct With 12 Different Shaped Vortex Generators

Abstract: Detailed local Nusselt number distributions in the first pass of a sharp turning two-pass square channel with various configurations of longitudinal vortex generator arranged on one wall were measured using transient liquid crystal thermography. Flow patterns and friction factors were measured by the use of laser-Doppler velocimeter and pressure transducer, respectively. The Reynolds number, based on channel hydraulic diameter and bulk mean velocity, was fixed at 1.2 × 10 4 . The vortex generator height-to-hydraulic diameter ratio and pitch-to-height ratio were 0.12 and 10, respectively. Comparisons in terms of heat transfer augmentation and uniformity and friction loss are first performed on 12 configurations of single longitudinal vortex generator. The fluid dynamic mechanisms and wall confinement relevant to heat transfer enhancement are then documented for three-selected vortex generator models. In addition, the differences in fluid flow and heat transfer characteristics between a single vortex generator and a vortex generator array are addressed for the delta wing I and 45 deg V (with tips facing upstream) models which provide better thermal performance among the 12 configurations examined

Wake Vortex Transport and Decay in Ground Effect: Vortex Linking with the Ground

Abstract: Numerical simulations are carried out with a three-dimensional Large-Eddy Simulation (LES) model to explore the sensitivity of vortex decay and transport in ground effect (IGE). The vortex decay rates are found to be strongly enhanced following maximum descent into ground effect. The nondimensional decay rate is found to be insensitive to the initial values of circulation, height, and vortex separation. The information gained from these simulations is used to construct a simple decay relationship. This relationship compares well with observed data from an IGE case study. Similarly, a relationship for lateral drift due to ground effect is constructed from the LES data. In the second part of this paper, vortex linking with the ground is investigated. Our numerical simulations of wake vortices for IGE show that a vortex may link with its image beneath the ground, if the intensity of the ambient turbulence is moderate to high. This linking with the ground (which is observed in real cases)gives the appearance of a vortex tube that bends to become vertically oriented and which terminates at the ground. From the simulations conducted, the linking time for vortices in the free atmosphere; i.e., a function of ambient turbulence intensity.

A DPIV study of the trailing vortex elements from the blades of a horizontal axis wind turbine in yaw

Abstract: Digital particle image velocimetry (DPIV) has been used in a wind tunnel study to measure the velocity field of the trailing vortices from the blades of a horizontal axis wind-turbine (HWAT) in yaw. The creation of the trailing vortex circulation is shown to vary as a function of the phase angle of the rotor and the angle of yaw between the wind and turbine rotor. The strength of the convecting vorticity was also shown to vary with time. The initial formation of the vortex is shown determined by the flow expansion angle while in yawed flows the developing vortex is then influenced by the vortex sheet shed from the inboard blade trailing edge. This interaction is shown to significantly affect the roll up of the tip vortex.

The evolution of vortices in vertical shear. III: Baroclinic vortices

Abstract: The evolution of baroclinic tropical-eye lone-like vortices in environmental vertical shear on an f-plane is investigated Idealized numerical calculations are performed using a primitive-equation model The vertical structure of the initial vortex is varied by changing the strength of the upper-level tangential wind The baroclinic vortices develop a vertical tilt and a cyclonic rotation of the mid-level centre about the surface centre occurs In most of the calculations the upper-level part of the vortex is advected away from the surface centre The motion of the upper-level part of the vortex can be attributed to advection by the flow associated with large-scale asymmetries in the potential vorticity and to the vertically penetrating flow associated with the potential vorticity of the lower portion of the tilted vortex As in the case of initially barotropic vortices the cyclonic rotation is found to depend on the parameters in the Rossby penetration depth The height at which the environmental flow is equal to the Speed of vortex motion is found to be higher for vortices with stronger flow at upper levels This is consistent with observations of tropical cyclones Significant changes in the potential-vorticity structure of the vortex occur, especially at upper levels The vortex becomes elliptic in shape and may extrude filaments of potential vorticily These filaments thin, and sometimes break away from the main vortex, which as a result becomes more symmetric The separation of the filaments from the main part of the vortex is often accompanied by a decrease in the vortex tilt A: some levels no filaments form and the elliptic vortex becomes more symmetric with time Calculations with a barotropic model show that both the potential-vorticity structure of the initial vortex, and the horizontally sheared flow associated with the vertical projection of the tilted potential-vorticity anomaly, play a role in the changes in the vortex Structure The development of potential-temperature asymmetries and an adiabatic vertical circulation are shown to be related to the direction of the vortex tilt This occurs even when the direction of tilt changes with height The changes in the low-level static stability associated with the vortex tilt are investigated and the implications for tropical-cyclone intensity change are discussed

Experiments on two-dimensional vortex patterns

Abstract: The evolution of a strongly magnetized electron system is identical to that of an ideal two-dimensional (2-D) fluid; an electron column is equivalent to a fluid vortex. We have studied the stability of 2-D vortex patterns with electron columns confined in a Malmberg–Penning trap. The following cases are presented: the stability of N vortices arranged in a ring; the stability of N vortices arranged in a ring with a central vortex; the stability of more complicated vortex patterns.

Effects of trailing jet instability on vortex ring formation

Abstract: Numerical simulations of an impulsively started jet were performed in order to investigate the effects of trailing jet instability on axisymmetric vortex ring formation. The predictions were compared to experimental results reported in the literature and to recently published numerical results. The total and vortex ring circulations were found to be in good agreement with both the experimental and the numerical results. The presence of a universal formation time scale was confirmed. The results also highlighted an important interaction between an instability which develops in the trailing jet for large discharge times and the dynamics of the head vortex ring. This interaction accelerates the process by which the vortex ring detaches from the trailing jet and has a significant effect on the vortex ring circulation.

Unsteady Flow Behavior due to Breakdown of Tip Leakage Vortex in an Axial Compressor Rotor at Near-Stall Condition

Abstract: The unsteady flow nature caused by the breakdown of the tip leakage vortex in an axial compressor rotor at near-stall conditions has been investigated by unsteady three-dimensional Navier-Stokes flow simulations. The simulations show that the spiral-type breakdown of the tip leakage vortex occurs inside the rotor passage at the near-stall conditions. Downstream of the breakdown onset, the tip leakage vortex twists and turns violently with time, thus interacting with the pressure surface of the adjacent blade. The motion of the vortex and its interaction with the pressure surface are cyclic. The vortex breakdown causes significant changes in the nature of the tip leakage vortex, which result in the anomalous phenomena in the time-averaged flow fields near the tip at the near-stall conditions: no rolling-up of the leakage vortex downstream of the rotor, disappearance of the casing wall pressure trough corresponding to the leakage vortex, large spread of the low-energy fluid accumulating on the pressure side, and large pressure fluctuation on the pressure side. As the flow rate is decreased, the movement of the tip leakage vortex due to its breakdown becomes so large that the leakage vortex interacts with the suction surface as well as the pressure one. The interaction with the suction surface gives rise to the three-dimensional separation of the suction surface boundary layer.© 2000 ASME

Vortex shedding and drag in dilute Bose-Einstein condensates

Abstract: Above a critical velocity, the dominant mechanism of energy transfer between a moving object and a dilute Bose-Einstein condensate is vortex formation. In this paper, we discuss the critical velocity for vortex formation and the link between vortex shedding and drag in both homogeneous and inhomogeneous condensates. We find that at supersonic velocities sound radiation also contributes significantly to the drag force.

Oscillation of Vortex Breakdown Location and Blowing Control of Time-Averaged Location

Abstract: : The goal of this research is the control of leading-edge vortex breakdown location utilizing along-the-core blowing near the apex on the leeward surface of sharp-edged, slender, delta wings at high angles of attack. In the S2Ch subsonic wind tunnel at ONERA Chalais Meudon, two delta wing models with 70-deg sweep angles and root chords of 950 mm have been configured to collect qualitative and quantitative surface and flowfield data. First, an examination of the streamwise, time-dependent oscillation of the leading-edge vortex breakdown locations without active flow control is presented. These results further the understanding of the vortex breakdown phenomena and provide a more precise basis for evaluating the effectiveness of various flow control methods. Second, open-loop blowing along one of the vortex cores on the leeward surface of the delta wing demonstrates the ability to displace downstream the controlled, time-averaged, vortex breakdown location by 20% of the root chord.

Measurements of Tip Vortex Characteristics and the Effect of an Anti-Cavitation Lip on a Model Kaplan Turbine Blade

Abstract: Motivated by the problem of cavitation erosion, the position and strength of the roll-up vortex on the suction side of a Kaplan-type turbine blade with various endings is investigated. Measurements are made on different models with simplified two-dimensional geometries using mainly particle image velocimetry. It is found that the greatest danger of cavitation erosion exists when the casing of the turbine is of the “semi-spherical” type, so that there is a large and closing clearance gap at the leading edge of the blade. Furthermore, the anti-cavitation lip used in this study is shown to be ineffective at increasing the distance of the vortex from the blade, although it does reduce the circulation of the vortex and presumably the danger of cavitation. Our measurements are found to be in good agreement with existing models for the position of the vortex when appropriately interpreted.

Turbulence structure and vortex dynamics

Abstract: Introduction 1. Motion and expansion of a viscous vortex ring: elliptical slowing down and diffusive expansion Yasuhide Fukumoto and H. K. Moffatt 2. Stretching and compression of vorticity in the 3D Euler equations J. D. Gibbon, B. Galanti and R. M. Kerr 3. Structure of a new family of vortices of stretched non-axisymmetric vortices Stephane le Dizes 4. Core dynamics of a coherent structure: a prototypical physical-space cascade mechanism? Dhoorjaty S. Pradeep and Fazle Hussain 5. Fundamental instabilities in spatially-developing wing wakes and temporally-developing vortex pairs C. H. K. Williamson, T. Leweke and G. D. Miller 6. Vortex lines and vortex triangles in superfluid helium Carlo F. Barenghi 7. Evolution of localized packets of vorticity and scalar in turbulence A. Leonard 8. Vortical structure and modelling of turbulence E. A. Novikov 9. The issue of local isotropy of velocity and scalar turbulent fields Z. Warhaft 10. Near-singular flow structure: dissipation and eduction J. C. Vassilicos 11. Vortex stretching versus production of strain/dissipation Arkaday Tsinober 12. Dynamics and statistics of vortical eddies in turbulence J. C. R. Hunt 13. Stability of vortex structures in a rotating frame Claude Cambon 14. LES and vortex topology in shear and rotating flows Marcel Lesieur, Pierre Comte and Olivier Metais 15. Conditional mode elimination with asymptotic freedom for isotropic turbulence at large Reynolds numbers David McComb and Craig Johnston.

A model for vortex ring formation in a starting buoyant plume

Abstract: Vortex ring formation in a starting axisymmetric buoyant plume is considered. A model describing the process is proposed and a physical explanation based on the Kelvin–Benjamin variational principle for steady vortex rings is provided. It is shown that Lundgren et al.'s (1992) time scale, the ratio of the velocity of a buoyant plume after it has travelled one diameter to its diameter, is equivalent to the time scale (formation time) proposed by Gharib et al. (1998) for uniform-density vortex rings generated with a piston/cylinder arrangement. It is also shown that, similarly to piston-generated vortex rings (Gharib et al. 1998), the buoyant vortex ring pinches off from the plume when the latter can no longer provide the energy required for steady vortex ring existence. The dimensionless time of the pinch-off (the formation number) can be reasonably well predicted by assuming that at pinch-of the vortex ring propagation velocity exceeds the plume velocity. The predictions of the model are compared with available experimental results.

Linear and nonlinear interactions between a columnar vortex and external turbulence

Abstract: The structure of initially isotropic homogeneous turbulence interacting with a columnar vortex (with circulation Γ and radius σ), idealized both as a solid cylinder and a hollow core model is analysed using the inhomogeneous form of linear rapid distortion theory (RDT), for flows where the r.m.s. turbulence velocity u0 is small compared with Γ/σ. The turbulent eddies with scale Γ are distorted by the mean velocity gradient and also, over a distance Γ from the surface of the vortex, by their direct impingement onto it, whether it is solid or hollow. The distortion of the azimuthal component of turbulent vorticity by the differential rotation in the mean flow around the columnar vortex causes the mean-square radial velocity away from the cylinder to increase as (Γt/2πr2)2 (Γx/r)u20, when (r − σ) > Γx, but on the surface of the vortices ((r − σ) < Γx) where 〈u2r〉 is reduced, 〈u2z〉 increases to the same order, while the other components do not grow. Statistically, while the vorticity field remains asymmetric, the velocity field of small-scale eddies near the vortex core rapidly becomes axisymmetric, within a period of two or three revolutions of the columnar vortex. Calculation of the distortion of small-scale initially random velocity fields shows how the turbulent eddies, as they are wrapped around the columnar vortex, become like vortex rings, with similar properties to those computed by Melander & Hussain (1993) using a fully nonlinear direct numerical simulation. A mechanism is proposed for how interactions between the external turbulence and the columnar vortex can lead to non-axisymmetric vortex waves being excited on the vortex and damped fluctuations in its interior. If the columnar vortex is not significantly distorted by these linear effects, estimates are made of how nonlinear effects lead to the formation of axisymmetric turbulent vortices which move as result of their image vorticity (in addition to the self-induction velocity) at a velocity of order u0tΓ/σ2 parallel to the vortex. Even when the circulation (γ) of the turbulent vortices is a small fraction of Γ, they can excite self-destructive displacements through resonance on a time scale σ/u0.

Vortex ring oscillations, the development of turbulence in vortex rings and generation of sound

Abstract: The state of the art in describing the eigen-oscillations of a vortex ring in an ideal incompressible fluid is reviewed. To describe eigen-oscillations, the displacement field is taken as the basic dynamic variable. A vortex ring with the simplest vorticity distribution in the core and with a potential flow in the vortex ring envelope is the commonest approximation used in treating the eigen-oscillations of vortex rings of a more general form. It turns out that allowing for even a very weak degree of core smoothing causes many oscillation modes to lose their stability. It is shown that the instability effect is determined by the sign of the vibration energy. The energies of the ring eigen-oscillations are calculated and two kinds of eigen-oscillations, those with a negative energy and those with a positive energy, are identified, of which it is the former which become unstable when the core vorticity is smoothed. The multiple instabilities of vortex ring oscillations together with the details of the spatial structure of its eigen-oscillations suggest that it is the nonlinear evolution of precisely these processes which might be the origin of vortex ring turbulence. A new method for the study of unsteady processes in turbulent vortex rings, which utilizes the experimental diagnostics of the ring's sound field, is presented. The structure of the sound field strongly supports the proposed model of the turbulent vortex ring.

Interaction of Barotropic Vortices with Coastal Topography: Laboratory Experiments and Numerical Simulations

Abstract: The interaction of a barotropic cyclonic vortex on a b plane with a strong topographic slope is studied by means of laboratory experiments and numerical simulations. In the laboratory, the vortex is produced in a rectangular rotating tank with a weak uniformly sloping bottom (slope angle 3.58) in order to simulate the b effect. The cyclonic vortex moves in the northwestward direction and interacts with an additional, pronounced linear topography (slope angle 358) along the western boundary of the tank. The laboratory experiments revealed that the original northwestward trajectory changes to the south until the vortex is dissipated by viscous effects and bottom friction. As it moves upslope, the exterior ring of the vortex forms a strong current to the northeast. From this current a new cyclonic vortex is created, repeating approximately the behavior of the original one. Later, two more vortices are formed in the same way. A finite difference numerical model is used to solve the nondivergent barotropic equation. Despite the presence of the strong slope, agreement between laboratory results and numerical runs suggests that conservation of potential vorticity is indeed the basic mechanism involved in the southward motion of the vortex and the northeastward meandering current.

Theoretical and computational aspects of the self-induced motion of three-dimensional vortex sheets

Abstract: Theoretical and computational aspects of the self-induced motion of closed and periodic three-dimensional vortex sheets situated at the interfaces between two inviscid uids with generally different densities in the presence of surface tension are considered. In the mathematical formulation, the vortex sheet is described by a continuous distribution of marker points that move with the velocity of the fluid normal to the vortex sheet while executing an arbitrary tangential motion. Evolution equations for the vectorial jump in the velocity across the vortex sheet, the vectorial strength of the vortex sheet, and the scalar circulation field or strength of the effective dipole field following the marker points are derived. The computation of the self-induced motion of the vortex sheet requires the accurate evaluation of the strongly singular Biot-Savart integral whose existence requires that the normal vector varies in a continuous fashion over the vortex sheet. Two methods of computing the principal value of the Biot-Savart integral are implemented. The first method involves computing the vector potential and the principal value of the harmonic potential over the vortex sheet, and then differentiating them in tangential directions to produce the normal or tangential component of the velocity, in the spirit of generalized vortex methods developed by Baker (1983). The second method involves subtracting off the dominant singularity of the Biot-Savart kernel and then accounting for its contribution by use of vector identities. Evaluating the strongly singular Biot-Savart integral is thus reduced to computing a weakly singular integral involving the mean curvature of the vortex sheet, and this allows the routine discretization of the vortex sheet into curved elements whose normal vector is not necessarily continuous across the edges, and the computation of the self-induced velocity without kernel desingularization. Numerical simulations of the motion of a closed or periodic vortex sheet immersed in a homogeneous fluid confirm the effectiveness of the numerical methods for a limited time of evolution. Numerical instabilities arise after a certain evolution time due to the ill-posedness of vortex sheet dynamics. The motion may be regularized by desingularizing the Biot-Savart kernel using either Krasny's (1986 b ) method or spectrum truncation. Depending, however, on the physical mechanism that drives the motion, the instabilities may persevere.

Sound generation by coaxial collision of two vortex rings

Abstract: Sound pressure fields generated by coaxial collisions of two vortex rings with equal/unequal strengths are simulated numerically. The axisymmetric, unsteady, compressible Navier--Stokes equations are solved by a finite difference method, not only for a near field but also for a far field. The sixth-order-accurate compact Pade scheme is used for spatial derivatives, together with the fourth-order-accurate Runge-Kutta scheme for time integration. The results show that the generation of sound is closely related to the change of direction of the vortex ring motion induced by the mutual interaction of the two vortex rings. For the case of equal strength (head-on collision), the change of direction is associated with stretching of the vortex rings. Generated sound waves consist of compression parts and rarefaction parts, and have a quadrupolar nature. For the case of unequal strengths, the two vortex rings pass through each other; the weaker vortex ring moves outside the stronger vortex ring which shows a loop motion. The number of generated waves depends on the relative strength of the two vortex rings. The sound pressure includes dipolar and octupolar components, in addition to monopolar and quadrupolar components which are observed for the case of a head-on collision.

Mass Transport by a Vortex Ring

Abstract: Mass transport by a vortex ring in water has been studied experimentally. A vortex ring with the Reynolds number in the vicinity of ∼1×10 5 is launched in water by means of an exploding wire. Fine particles injected into a vortex ring at the outlet of vortex driver are carried away with vortex motion. Some particles spin out of the vortex motion and are left behind a vortex ring. But many of them are trapped in a vortex ring and are carried up to the end of water tank which is located at 1.4 m from the vortex driver. Mass analyses of particles show that particles with specific gravity of larger than unity are scattered out of a vortex ring due to a centrifugal force, but those with specific gravity being less than unity are trapped in a vortex core and are carried for a long distance. The result indicates that an efficient mass transport by a vortex ring is realized when the specific gravity of particles is less than that of ambient fluid that supports a vortex ring.

Vortex formation in front of a piston moving through a cylinder

Abstract: This paper contains the details of an experimental study of the vortex formed in front of a piston as it moves through a cylinder. The mechanism for the formation of this vortex is the removal of the boundary layer forming on the cylinder wall in front of the advancing piston. The trajectory of the vortex core and the vorticity distribution on the developing vortex have been measured for a range of piston velocities. Velocity field measurements indicate that the vortex is essentially an inviscid structure at the Reynolds numbers considered, with viscous effects limited to the immediate corner region. Inviscid flow is defined in this paper as being a region of the flow where inertial forces are significantly larger than viscous forces. Flow visualization and vorticity measurements show that the vortex is composed mainly of material from the boundary layer forming over the cylinder wall. The characteristic dimension of the vortex appears to scale in a self-similar fashion, while it is small in relation to the apparatus length scale. This scaling rate of t0.85+0.7m, where the piston speed is described as a power law Atm, is somewhat faster than the t3/4 scaling predicted by Tabaczynski et al. (1970) and considerably faster than a viscous scaling rate of t1/2. The reason for the structure scaling more rapidly than predicted is the self-induced effect of the secondary vorticity that is generated on the piston face. The vorticity distribution shows a distinct spiral structure that is smoothed by the action of viscosity. The strength of the separated vortex also appears to scale in a self-similar fashion as t2m+1. This rate is the same as suggested from a simple model of the flow that approximates the vorticity being ejected from the corner as being equivalent to the flux of vorticity over a flat plate started from rest. However, the strength of the vorticity on the separated structure is 25% of that suggested by this model, sometimes referred to as the ‘slug’ model. Results show that significant secondary vorticity is generated on the piston face, forming in response to the separating primary vortex. This secondary vorticity grows at the same rate as the primary vorticity and is wrapped around the outside of the primary structure and causes it to advect away from the piston surface.

Velocity Measurements on a Delta Wing with Periodic Blowing and Suction

Abstract: The mechanism by which periodic blowing and suction at the leading edge improves lift and stall angle of a 70° sweep delta wing is investigated in water tunnel experiments using PIV measurements. Periodic sinusoidal blowing and suction with zero net mass flux is applied at the leading edge of the wing. The experiments were conducted at a freestream flow speed of 0.126 m/s, corresponding to a root chord Reynolds number of 25,000. The wing was kept at an angle of attack of 35° for this study. A forcing frequency of F" = 1.75 was used, which was shown in previous research to be most effective in improving lift. The momentum coefficient was kept constant at (Cjii) of 0.004. The two main vortices that dominate the unforced flow field are stationary without forcing. With forcing, however, the vortex centers travel both in spanwise and wing normal direction along an elliptic path. The streamwise vortex breakdown location is not changed as determined by measurements of the streamwise vorticity component. Instead, the forcing increases the axial velocity downstream of the vortex breakdown location, thus decreasing the local surface pressure and increasing normal force. This effect is attributed to the formation of a shear layer vortex during the blowing cycle, which carries high momentum fluid into the wake left downstream of the main vortex breakdown. The wake is weakened in synchronization with the presence of the shear layer vortex through the forcing cycle.

Experimental dynamics of a vortex within a vortex.

Abstract: We report the experimental dynamics of a new two-dimensional (2D) fluid phenomenon that occurs when an intense, pointlike vortex is placed within a diffuse, circular vortex. Our observations, made using strongly magnetized electron columns to model the 2D fluid, support the analysis performed by Jin and Dubin.

Sound sources in the interactions of two inviscid two-dimensional vortex pairs

Abstract: The sources of sound during the interactions of two identical two-dimensional inviscid vortex pairs are investigated numerically by using the vortex sound theory and the method of contour dynamics. The sound sources are identified and then separated into two independent components, which represent the contributions from the vortex centroid dynamics and the microscopic vortex core dynamics. Results show that the sound generation mechanism of the latter is independent of the type of vortex pair interaction, while that of the former depends on the jerks, accelerations and vortex forces on the vortex pairs. The power developed by the vortex forces is found to be important in the generation of sound when the vortex cores are severely deformed and their centroids are close to each other. The isolated source terms also explain the appearance of wavy oscillations on the time variations of the sound source strengths in the vortex ring and the two-dimensional vortex interaction systems.