Contour dynamics in complex domains

Crowdy, Darren; Surana, Amit

doi:10.1017/s002211200700866x

Cited by 27 publications

(20 citation statements)

References 32 publications

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“…Once the region of concavity reached the corner near the front of the vortex, it led to the formation of a small mound on the contour, which rapidly developed into a vortex filament. The filamentation of a sufficiently perturbed vortex has been observed consistently in previous studies (Deem & Zabusky 1978;Dritschel 1988a,b;Saffman 1992;Crowdy & Surana 2007), and as such the emission of a filament by these perturbed Norbury vortices is to be expected. What is particular to these vortices is the development of the filament consistently at the location of the region of initial concavity, by the mechanism described above.…”

Section: Response Of the Norbury Family Of Vortex Ringssupporting

confidence: 78%

“…Eventually, the formation of small mounds on the core boundary led to the development of thin filaments, which wrapped around the vortex core. 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.…”

Section: Response Of the Norbury Family Of Vortex Ringsmentioning

confidence: 98%

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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 Ringssupporting

confidence: 78%

Section: Response Of the Norbury Family Of Vortex Ringsmentioning

confidence: 98%

Perturbation response and pinch-off of vortex rings and dipoles

O’Farrell

Dabiri

2012

J. Fluid Mech.

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“…This calculation implies the use of the Green function G(x, y; x 0 , y 0 ), which can be interpreted as the stream function of a flow induced by a unit point vortex located at a point (x 0 , y 0 ) on the (x, y)-plane, and computation of contour integrals over the patch boundaries. The construction of the Green function in complex domains is often facilitated by the use of image vortices (Coppa, Peano & Peinetti 2002;Johnson & McDonald 2004;Elcrat, Fornberg & Miller 2005;Crowdy & Surana 2007). For a plane with a circular cutout of unit radius centred at the origin of the frame of reference, a Green function can be written as Makarov, L. Kamp and G. van Heijst (e.g.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Instabilities of the flow around a cylinder and emission of vortex dipoles

Kizner

Makarov²,

Kamp

et al. 2013

J. Fluid Mech.

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Instabilities and long-term evolution of two-dimensional circular flows around a rigid circular cylinder (island) are studied analytically and numerically. For that we consider a base flow consisting of two concentric neighbouring rings of uniform but different vorticity, with the inner ring touching the cylinder. We first study the inviscid linear stability of such flows to perturbations of the free edges of the rings. For a given ratio of the vorticity in the rings, the governing parameters of the problem are the radii of the inner and outer rings scaled on the cylinder radius. In this two-dimensional parameter space, we determine analytically the regions of linear stability/instability of each azimuthal mode m = 1, 2, . . . . In the physically most meaningful case of zero net circulation, for each mode m > 1, two regions are identified: a regular instability region where mode m is unstable along with some other modes, and a unique instability region where only mode m is unstable. After the conditions of linear instability are established, inviscid contour-dynamics and high-Reynolds-number finite-element simulations are conducted. In the regular instability regions, simulations of both kinds typically result in the formation of vortical dipoles or multipoles. In the unique instability regions, where the inner vorticity ring is much thinner than the outer ring, the inviscid contour-dynamics simulations do not reveal dipole emission. In the viscous simulation, because viscosity has time to widen the inner ring, the instability develops in the same manner as in the regular instability regions.

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“…The two fields superpose to give the unique total velocity for advancing the flow. The alternative approach 19 presented here avoids the supplementary computations by modifying the Green's function in the contour dynamics integrations (as has been done for channel flow 20 and geometries that can be conformally mapped to a simpler circular domain 21 ). This method applies to circular topography with finite depth changes and also extends to free-surface flows where the governing equation is the inhomogeneous Helmholtz equation instead of the Poisson's equation considered here.…”

Section: The Green's Functionmentioning

confidence: 99%

Beach vortices near circular topography

2016

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Finite-area monopolar vortices which propagate around topography without change in shape are computed for circular seamounts and wells including the limiting cases of each: islands and infinitely deep wells. The time-dependent behaviour of vortex pairs propagating toward circular topography is also examined. Trajectories of point-vortex pairs exterior to the topography are found and compared to trajectories of vortex patches computed using contour dynamics.

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Contour dynamics in complex domains

Cited by 27 publications

References 32 publications

Perturbation response and pinch-off of vortex rings and dipoles

Perturbation response and pinch-off of vortex rings and dipoles

Instabilities of the flow around a cylinder and emission of vortex dipoles

Beach vortices near circular topography

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