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@article{Nelson:2021:10.1017/jfm.2020.803,
author = {Nelson, R and Krishnamurthy, V and Crowdy, D},
doi = {10.1017/jfm.2020.803},
journal = {Journal of Fluid Mechanics},
title = {The corotating hollow vortex pair: steady merger and break-up via a topological singularity},
url = {http://dx.doi.org/10.1017/jfm.2020.803},
volume = {907},
year = {2021}
}

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TY  - JOUR
AB  - The shapes of two steadily rotating, equal circulation, two-dimensional hollow vortices are determined and their properties examined. By means of a numerical scheme that accounts for the doubly connected nature of the fluid domain, it is shown that a one-parameter family of solutions exists that is a continuation of a corotating point vortex pair. Withb= 2 set as the distance between the vortex centroids we find that each vortex reaches a maximum possible area of 0.796 corresponding toa/b= 0.260 where a is a measure of the vortex core radius proposed by Meunieret al[Phys. Fluids,14, (2002)]. Results are compared to those of a previous study by Saffman & Szeto [Phys. Fluids,23, (1980)] in which two corotating patches of uniform vorticity are considered in place of the hollow vortices studied here. The general behaviour of the two systems is seen to be similar but some differences are highlighted, especially when the vortices become close to touching due to the accumulation of vorticity in thin extended fingers emanating from each of the vortices. The numerical scheme captures the family of equilibria very close to a critical configuration where these fingers tend to touch at the centre of rotation corresponding to a/b≈0.283.  By  a  simple  adaptation  of  the  numerical  scheme  to  compute  2-fold rotationally symmetric equilibria for a single rotating hollow vortex we then show that its limiting configuration is one where a thin waist forms leading to two separate parts of  its  single  boundary  drawing  close  together.  We  give  evidence  that  the  limit  of  this single vortex configuration coincides with the limit of the two-vortex configuration. The limiting  configuration  itself  turns  out  not  to  be  physically  admissible  leading  to  what we refer to as a topological singularity since no physical quantities blow up, indeed they appear to be continuous as the limiting state is approached from the two topologically distinct directions.
AU  - Nelson,R
AU  - Krishnamurthy,V
AU  - Crowdy,D
DO  - 10.1017/jfm.2020.803
PY  - 2021///
SN  - 0022-1120
TI  - The corotating hollow vortex pair: steady merger and break-up via a topological singularity
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2020.803
UR  - http://hdl.handle.net/10044/1/83599
VL  - 907
ER  -

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