1995
DOI: 10.1063/1.868602
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Unsteady evolutions of vortex rings

Abstract: Unsteady evolutions of vortex rings with linearly distributed vorticity and various core parameters are considered in an unbounded, inviscid fluid. The instability of a Norbury vortex with a moderate core thickness parameter α is also investigated. Contour integral expressions based on the Biot–Savart law for the velocity field induced by a vortex ring are derived. Numerical results show that all vortex rings except the Norbury vortices will undergo an unsteady evolution process to reach an asymptotic state. T… Show more

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Cited by 10 publications
(12 citation statements)
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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%
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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%
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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%