Barotropic elliptical dipoles in a rotating fluid

Trieling, RR Ruben; Santbergen, Rudi; Heijst, Gjf Gert-Jan van; Kizner, Ziv

doi:10.1007/s00162-009-0133-6

Cited by 6 publications

(2 citation statements)

References 8 publications

(9 reference statements)

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“…Dipolar vortices have been observed experimentally in flows in which three-dimensional motions have been suppressed by stratification (van Heijst & Flór 1989), by utilizing a thin soap film (Couder & Basdevant 1986;Afanasyev 2006), by rotation of the ambient fluid (Velasco Fuentes & van Heijst 1994;Trieling et al 2010), or by the imposition of a magnetic field on a layer of mercury (Nguyen Duc & Sommeria 1998). In these experiments and in computational studies (van Geffen & van Heijst 1998;DuranMatute et al 2010;Pedrizzetti 2010), thick-cored, nearly symmetry-axis-touching dipoles were often observed, leading to speculation that the physical constraint on vortex growth identified by Gharib et al (1998) for axisymmetric vortex rings does not extend to two-dimensional vortex pairs.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Perturbation response and pinch-off of vortex rings and dipoles

O’Farrell

Dabiri

2012

J. Fluid Mech.

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“…Vortex dipoles can transport water and its content for many kilometers. It is therefore both important and interesting to analyse the regular and chaotic dynamics they exhibit [12][13][14][15][16][17][18][19][20][21][22][23][24] . The evolution of a pair of uniform vorticity patches has been the topic of many previous works [25][26][27][28] .…”

Section: Introductionmentioning

confidence: 99%

Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

2018

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We investigate the evolution of a pair of two-dimensional, opposite-signed, finitesize vortices interacting with a fixed point vortex. The present paper builds on the accompanying study [Koshel, K. V., Reinaud, J. N., Riccardi, G. and Ryzhov, E. A. Phys. Fluids (2018)] focusing on the motion of a pair of point vortices impinging on a fixed point vortex. Here, in contrast, the pair of opposite-signed finite-size vortices, or vortex dipole for simplicity, can deform. This deformation has an impact on the dynamics. We show that, as expected, finite size vortices behave like point vortices if they are distant enough from each other. This allows one to recover the rich and diverse set of possible trajectories for the dipole. This includes the regimes of intricate bounded motion when the finite-size vortices remain stable near the fixed vortex for a long time. On the other hand, we show that large finite-size vortices can deform significantly and deviate from the trajectories of equivalent point vortices. When the shear that the vortices induce on each other is large enough, the finite size vortices may break into smaller structures or may even be completely strained out.

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Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

O’Farrell

Dabiri

2014

J. Fluid Mech.

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Inviscid models for vortex rings and dipoles are constructed using nested patches of vorticity. These models constitute more rcalislic approximations to experimcncal vortex rings and dipoles than the single-contour models of Norbury and Pierrehumbert, and nested contour dynamics algorithms allow their simulation with low computational cost. In two dimensions, nested-contour models for the analytical Lamb dipole are constructed. In the axisymmetric case, a family of models for vortex rings generated by a piston-cylinder apparatus at different stroke ratios is constructed from experimental data. The perturbation response of this family is considered by the introduction of a small region of vorticity at the rear of the vortex, which mimics the addition of circulation to a growing vortex ring by a feeding shear layer. Model vortex rings are found to either accept the additional circu lation or shed vorticity into a tail, depending on the perturbation size. A change in the behaviour of the model vortex rings is identified at a stroke ratio of three, when it is found that the maximum relative perturbation size vortex rings can accept becomes approximately constant. We hypothesise that this change in response is related to p inch-off, and that pinch-off might be understood and predicted based on the perturbation responses of model vortex rings. In particu lar, we suggest that a perturbation response-based framework can be useful in understanding vortex formation in biological flows.

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Barotropic elliptical dipoles in a rotating fluid

Cited by 6 publications

References 8 publications

Perturbation response and pinch-off of vortex rings and dipoles

Perturbation response and pinch-off of vortex rings and dipoles

Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

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