2019
DOI: 10.1017/jfm.2019.502
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Steady point vortex pair in a field of Stuart-type vorticity

Abstract: A new family of exact solutions to the two-dimensional steady incompressible Euler equation is presented. The solutions provide a class of hybrid equilibria comprising two point vortices of unit circulation – a point vortex pair – embedded in a smooth sea of non-zero vorticity of ‘Stuart-type’ so that the vorticity $\unicode[STIX]{x1D714}$ and the stream function $\unicode[STIX]{x1D713}$ are related by $\unicode[STIX]{x1D7… Show more

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Cited by 8 publications
(21 citation statements)
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References 21 publications
(33 reference statements)
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“…2003; Celli, Lacomba & Pérez-Chavela 2011) and generalized vortices of finite area (Crowdy 1999; Crowdy & Cloke 2002; Crowdy 2003; Krishnamurthy et al. 2019). Vortex arrays have also been observed in magnetized non-neutral plasmas (Schecter et al.…”
Section: Introductionmentioning
confidence: 99%
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“…2003; Celli, Lacomba & Pérez-Chavela 2011) and generalized vortices of finite area (Crowdy 1999; Crowdy & Cloke 2002; Crowdy 2003; Krishnamurthy et al. 2019). Vortex arrays have also been observed in magnetized non-neutral plasmas (Schecter et al.…”
Section: Introductionmentioning
confidence: 99%
“…In fluid mechanics, rings composed of multiple vortices are of particular interest and have been observed over a broad range of scales, from baths of superfluid helium (Yarmchuk, Gordon & Packard 1979) to hurricane eyewalls (Kossin & Schubert 2004). Several theoretical studies have characterized the stability of polygonal vortex arrays composed of both point vortices (Thomson 1883;Havelock 1931;Aref et al 2003;Celli, Lacomba & Pérez-Chavela 2011) and generalized vortices of finite area (Crowdy 1999;Crowdy & Cloke 2002;Crowdy 2003;Krishnamurthy et al 2019). Vortex arrays have also been observed in magnetized non-neutral plasmas (Schecter et al 1999;Durkin & Fajans 2000) and in both bosonic and fermionic systems, where vortices play a critical role in superconductivity (Saarikoski et al 2010).…”
Section: Introductionmentioning
confidence: 99%
“…These ideas can be extended to obtain Stuart vortex solutions on a torus (Sakajo 2019) and on a hyperbolic sphere (Yoon, Yim & Kim 2020). The introduction in Krishnamurthy et al (2019) discusses other applications and extensions of Stuart vortices.…”
mentioning
confidence: 99%
“…In these cases, invoking symmetry arguments is sufficient to ensure that the point vortices are stationary, and the solutions obtained are therefore steady. In a recent paper, Krishnamurthy et al (2019) showed the existence of an asymmetric family of hybrid vortex equilibria (although the background field is referred to there as 'Stuart-type' vorticity in deference to Stuart 1967). They showed that a colinear three point vortex equilibrium, which is a limiting case of the N = 2 hybrid equilibrium discussed in Crowdy (2003), can be continuously deformed into another non-trivial family of hybrid equilibria comprising a point vortex pair in equilibrium in an ambient field of Liouville-type vorticity.…”
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confidence: 99%
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