## Abstract

This paper examines the stability of vortices in a two-layer ocean on the f-plane. The mean depth h̄_{1} of the upper layer is assumed to be much smaller than the depth h̄_{2} of the lower layer. Using the primitive equations, we derive an asymptotic criterion for baroclinic instability of compensated (i.e. confined to the upper layer) vortices. Surprisingly, it coincides exactly with a similar criterion derived from the quasigeostrophic equations [Benilov, E.S., 2003. Instability of quasigeostrophic vortices in a two-layer ocean with thin upper layer. J. Fluid Mech. 475, 303-331]. Thus, to leading order in h̄_{1}/h̄_{2}, ageostrophy does not affect the stability properties of thin compensated vortices. As a result, whether a vortex is stable or not, depends on its shape, not amplitude (although the growth rate of an unstable vortex does depend on its amplitude).

Original language | English |
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Pages (from-to) | 211-226 |

Number of pages | 16 |

Journal | Dynamics of Atmospheres and Oceans |

Volume | 39 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - May 2005 |

## Keywords

- Ageostrophy
- Baroclinic instability
- Ocean vortices