### Abstract

This paper examines the evolution of a two-dimensional vortex which initially consists of an axisymmetric monopole vortex with a perturbation of azimuthal wavenumber m = 2
added to it. If the perturbation is weak then the vortex returns to an axisymmetric state and the non-zero Fourier harmonics generated by the perturbation decay to zero.
However, if a finite perturbation threshold is exceeded, then a persistent nonlinear vortex structure is formed. This structure consists of a coherent vortex core with two satellites rotating around it.
The paper considers the formation of these satellites by taking an asymptotic limit in which a compact vortex is surrounded by a weak skirt of vorticity. The resulting equations match the behaviour of a normal mode riding on the vortex with the evolution of fine-scale vorticity in a critical layer inside the skirt. Three estimates of inviscid thresholds for the formation of satellites are computed and compared: two estimates use qualitative
diagnostics, the appearance of an infection point or neutral mode in the mean profile. The other is determined quantitatively by solving the normal mode/critical-layer equations numerically. These calculations are supported by simulations of the full Navier-Stokes equations using a family of proles based on the tanh function.

Original language | English |
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Pages (from-to) | 381-405 |

Number of pages | 25 |

Journal | Journal of Fluid Mechanics |

Volume | 614 |

DOIs | |

Publication status | Published - 2008 |

### Bibliographical note

© The Author(s) and Cambridge University Press, 2008## Fingerprint Dive into the research topics of 'Thresholds for the formation of satellites in two-dimensional vortices'. Together they form a unique fingerprint.

## Cite this

Turner, M. R., & Gilbert, A. D. (2008). Thresholds for the formation of satellites in two-dimensional vortices.

*Journal of Fluid Mechanics*,*614*, 381-405. https://doi.org/10.1017/S0022112008003558