Unsteady evolutions of vortex rings

Quyuan, Ye; Chu, C. K.

doi:10.1063/1.868602

Cited by 10 publications

(12 citation statements)

References 8 publications

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“…The filamentation of the vortex is a common feature in vortex dynamics, and it is observed even in linearly stable configurations (Deem & Zabusky 1978;Dritschel 1988a,b;Saffman 1992;Crowdy & Surana 2007). Thus, Pozrikidis (1986) and Ye & Chu (1995) remark that the appearance of thin filaments is of negligible importance to the dynamics of the perturbed vortex. Figure 5 depicts the evolution of a Norbury vortex with α = 0.5 subject to a perturbation of δ = −0.05.…”

Section: Response Of the Norbury Family Of Vortex Ringsmentioning

confidence: 97%

“…For consistency with the previous studies by Pozrikidis (1986) and Ye & Chu (1995), the factor γ (α, δ) was introduced in order to preserve the unperturbed core circulation. For each member of the family and perturbation size δ analytical expressions for the circulation of the perturbed and unperturbed vortices were obtained by integrating the vorticity over the regions described by (2.4) and (2.5)-(2.7).…”

Section: Shape Perturbationsmentioning

confidence: 99%

“…Gharib et al (1998) noted that this circulation shedding is analogous to pinch-off. In contrast, Ye & Chu (1995) investigated the response of a member of the Norbury family of moderate core thickness to similar shape perturbations, and found no evidence of tail shedding. However, the nonlinear response of the remainder of the Norbury family to prolate shape perturbations is unknown, and the transition from the observations of Ye & Chu (1995) to those of Pozrikidis (1986) has not been previously characterized.…”

Section: Introductionmentioning

confidence: 99%

“…However, they are of interest because the perturbations experienced by forming vortex rings and dipoles in an experimental setting are also not of the type described by Benjamin (1976). The response of the entire Norbury family to this type of perturbations was considered, in order to bridge the gap between the observations of Ye & Chu (1995) for thin-cored rings and those of Pozrikidis (1986) for Hill's spherical vortex. In particular, we searched for a change in the perturbation response as we considered vortex rings of increasing core thickness.…”

Section: Introductionmentioning

confidence: 99%

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Perturbation response and pinch-off of vortex rings and dipoles

O’Farrell

Dabiri

2012

J. Fluid Mech.

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The nonlinear perturbation response of two families of vortices, the Norbury family of axisymmetric vortex rings and the Pierrehumbert family of two-dimensional vortex pairs, is considered. Members of both families are subjected to prolate shape perturbations similar to those previously introduced to Hill's spherical vortex, and their response is computed using contour dynamics algorithms. The response of the entire Norbury family to this class of perturbations is considered, in order to bridge the gap between past observations of the behaviour of thin-cored members of the family and that of Hill's spherical vortex. The behaviour of the Norbury family is contrasted with the response of the analogous two-dimensional family of Pierrehumbert vortex pairs. It is found that the Norbury family exhibits a change in perturbation response as members of the family with progressively thicker cores are considered. Thin-cored vortices are found to undergo quasi-periodic deformations of the core shape, but detrain no circulation into their wake. In contrast, thicker-cored Norbury vortices are found to detrain excess rotational fluid into a trailing vortex tail. This behaviour is found to be in agreement with previous results for Hill's spherical vortex, as well as with observations of pinch-off of experimentally generated vortex rings at long formation times. In contrast, the detrainment of circulation that is characteristic of pinch-off is not observed for Pierrehumbert vortex pairs of any core size. These observations are in agreement with recent studies that contrast the formation of vortices in two and three dimensions. We hypothesize that transitions in vortex formation, such as those occurring between wake shedding modes and in vortex pinch-off more generally, might be understood and possibly predicted based on the observed perturbation responses of forming vortex rings or dipoles.

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Section: Response Of the Norbury Family Of Vortex Ringsmentioning

confidence: 97%

Section: Shape Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Perturbation response and pinch-off of vortex rings and dipoles

O’Farrell

Dabiri

2012

J. Fluid Mech.

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“…Several previous investigators have shown that oscillations can occur in the translation velocity of a vortex ring and are related to oscillations in the shape of the core. In particular, Moore (1980) showed that a vortex ring with a rotating core of elliptic cross-section has a time-periodic translation velocity, and Ye & Chu (1995) showed that a perturbed Norbury vortex ring has oscillations in the translation velocity and the shape of the core. In view of these results, the oscillation in the pair/ring translation velocity displayed in figure 9 may indicate that an oscillation is occurring in the shape of the vortex core.…”

Section: Quasi-steady Statementioning

confidence: 99%

The onset of chaos in vortex sheet flow

Krasny

Nitsche

2002

J. Fluid Mech.

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Regularized point-vortex simulations are presented for vortex sheet motion in planar and axisymmetric flow. The sheet forms a vortex pair in the planar case and a vortex ring in the axisymmetric case. Initially the sheet rolls up into a smooth spiral, but irregular small-scale features develop later in time: gaps and folds appear in the spiral core and a thin wake is shed behind the vortex ring. These features are due to the onset of chaos in the vortex sheet flow. Numerical evidence and qualitative theoretical arguments are presented to support this conclusion. Past the initial transient the flow enters a quasi-steady state in which the vortex core undergoes a small-amplitude oscillation about a steady mean. The oscillation is a time-dependent variation in the elliptic deformation of the core vorticity contours; it is nearly time-periodic, but over long times it exhibits period-doubling and transitions between rotation and nutation. A spectral analysis is performed to determine the fundamental oscillation frequency and this is used to construct a Poincaré section of the vortex sheet flow. The resulting section displays the generic features of a chaotic Hamiltonian system, resonance bands and a heteroclinic tangle, and these features are well-correlated with the irregular features in the shape of the vortex sheet. The Poincaré section also has KAM curves bounding regions of integrable dynamics in which the sheet rolls up smoothly. The chaos seen here is induced by a self-sustained oscillation in the vortex core rather than external forcing. Several well-known vortex models are cited to justify and interpret the results.

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Coaxial interactions of two vortex rings or of a ring with a body

Quyuan

Chiakun

1995

Acta Mech Sinica

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Unsteady evolutions of vortex rings

Cited by 10 publications

References 8 publications

Perturbation response and pinch-off of vortex rings and dipoles

Perturbation response and pinch-off of vortex rings and dipoles

The onset of chaos in vortex sheet flow

Coaxial interactions of two vortex rings or of a ring with a body

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