Interaction of Two Vortex Rings Moving along a Common Axis of Symmetry

Oshima, Yuko; Kambe, Tsutomu; Asaka, Saburo

doi:10.1143/jpsj.38.1159

Cited by 54 publications

(27 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This steplike increase was caused by the leading vortex in the trailing wake ͑hereafter referred to as vortex 2͒ catching up to and coalescing with the original vortex ring ͑hereafter referred to as vortex 1͒. 1,[26][27][28] In Fig. 5 we observe a similar steplike behavior after formation times of Ϸ10.…”

Section: A Vortex Pinch-offmentioning

confidence: 69%

A Lagrangian approach to identifying vortex pinch-off

O’Farrell

Dabiri

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

A criterion for identifying vortex ring pinch-off based on the Lagrangian coherent structures ͑LCSs͒ in the flow is proposed and demonstrated for a piston-cylinder arrangement with a piston stroke to diameter ͑L / D͒ ratio of Ϸ12. It is found that the appearance of a new disconnected LCS and the termination of the original LCS are indicative of the initiation of vortex pinch-off. The subsequent growth of new LCSs, which tend to roll into spirals, indicates the formation of new vortex cores in the trailing shear layer. Using this criterion, the formation number is found to be 4.1Ϯ 0.1, which is consistent with the predicted formation number of Ϸ4 of Gharib et al. ͓J. Fluid Mech. 360, 121 ͑1998͔͒. The results obtained using the proposed LCS criterion are compared with those obtained using the circulation criterion of Gharib et al. and are found to be in excellent agreement. The LCS approach is also compared against other metrics, both Lagrangian and Eulerian, and is found to yield insight into the pinch-off process that these do not. Furthermore, the LCS analysis reveals a consistent pattern of coalescing or "pairing" of adjacent vortices in the trailing shear layer, a process which has been extensively documented in circular jets. Given that LCSs are objective and insensitive to local errors in the velocity field, the proposed criterion has the potential to be a robust tool for pinch-off identification. In particular, it may prove useful in the study of unsteady and low Reynolds number flows, where conventional methods based on vorticity prove difficult to use. © 2010 American Institute of Physics. ͓doi:10.1063/1.3275499͔The formation of axisymmetric vortex rings is a widely occurring phenomenon both in nature and in industry. It is known that these vortex rings cannot grow indefinitely, but rather there is a physical limit to their size.1 Beyond this limit, vortex rings do not grow any further but "pinch off," and a trailing jet forms behind them. This limit implies the existence of an optimum vortex size: for optimum momentum transfer, rings must be made as large as possible while avoiding pinch-off.2 This optimum has important implications for natural and engineering flows, and hence vortex ring pinch-off has been extensively studied, principally by means of the vorticity field. However, in the more complex naturally occurring flows, the vorticity field tends to break down and diffuse, and existing criteria prove insufficient for robustly identifying pinch-off. In this paper we propose a criterion for pinchoff identification, based on Lagrangian coherent structures (LCSs), which could provide further insight into the structure of these complex natural flows. The criterion is demonstrated for a laboratory-generated vortex ring, and it is found to be in good agreement with the established criterion based on circulation.

show abstract

Section: A Vortex Pinch-offmentioning

confidence: 69%

A Lagrangian approach to identifying vortex pinch-off

O’Farrell

Dabiri

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…At low Reynolds numbers, reconnection occurs in a seemingly simple (laminar) way [35][36][37][38][39]. The process can be described by an elegant model [40], which very successfully reproduces the main features observed in low-resolution numerical studies [41].…”

Section: Discussionmentioning

confidence: 79%

Potential singularity mechanism for the Euler equations

2016

View full text Add to dashboard Cite

Singular solutions to the Euler equations could provide essential insight into the formation of very small scales in highly turbulent flows. Previous attempts to find singular flow structures have proven inconclusive. We reconsider the problem of interacting vortex tubes, for which it has long been observed that the flattening of the vortices inhibits sustained self-amplification of velocity gradients. Here we consider an iterative mechanism, based on the transformation of vortex filaments into sheets and their subsequent instability back into filaments. Elementary fluid mechanical arguments are provided to support the formation of a singular structure via this iterated mechanism, which we analyze based on a simplified model of filament interactions.

show abstract

“…Finally, one ring was approximated by the set of 12,100 vector vorticity particles. At first we tried to reproduce the leap-frogging ("vortex game") phenomenon [7,11,14]. When two co-axial vortex rings are made to travel in the same direction the velocity field induced by the second ring will cause the first ring to contract and accelerate.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…where C = 0.269 was calculated by us in order to satisfy the condition (11). That guarantees that the PSE method is second order.…”

Section: Equations Of Motion and Description Of The Vortex-in-cell Mementioning

confidence: 99%

Vorticity Particle Method for Simulation of 3D Flow

Kudela

Regucki

2004

Computational Science - ICCS 2004

View full text Add to dashboard Cite

Abstract. The vortex-in-cell method for three-dimensional, viscous flow was presented. A viscous splitting algorithm was used. Initially the Euler inviscid equation was solved. Following that, the viscous effect was taken into account by the solution of the diffusion equation. The diffusion equation was then solved by the particle strength exchange (PSE) method. Validation of the method was tested by simulation of the leapfrogging phenomenon for two vortex rings moving along a common axis of symmetry and the reconnection phenomenon of two colliding vortex rings for viscous flow.

show abstract

Interaction of Two Vortex Rings Moving along a Common Axis of Symmetry

Cited by 54 publications

References 5 publications

A Lagrangian approach to identifying vortex pinch-off

A Lagrangian approach to identifying vortex pinch-off

Potential singularity mechanism for the Euler equations

Vorticity Particle Method for Simulation of 3D Flow

Contact Info

Product

Resources

About