### Abstract

Reduced gravity models, namely, those having an active layer of fluid floating on top of a motionless one, have been largely used to study the upper ocean. This approximation is formally valid when the total ocean depth tends to infinity. The effect of a finite ocean depth on the upper ocean baroclinic instability is examined here using a quasi-geostrophic three-layer model and comparing the results with those obtained using a reduced gravity quasi-geostrophic two-layer model or 2.5-layer model. The basic state is a zonal current with uniform velocities within each layer. The ratio ε between the sum of the upper two layers mean depths and the lower layer mean depth is the relevant new parameter of the problem. Even for very small values of ε, important differences between the 2.5-layer (ε = 0) and the three-layer (ε > 0) model are found. As ε increases, the region of Arnold stable states decreases. For certain basic states, new normal mode instability branches are found, whose growth rates increase with ε. An asymptotic expansion in ε is made in order to shed some light on the transition regime between both models. This allows one to interpret the new instabilities as a consequence of the resonant interplay between the stable modes in the 2.5-layer model and a short Rossby wave in the deep layer. The growth rates of the new instability branches are O(ε^{1/3}) and O(ε^{1/2}) and cannot be neglected even for reasonably small values of ε.

Original language | English (US) |
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Article number | 2000JC000666 |

Pages (from-to) | 26863-26877 |

Number of pages | 15 |

Journal | Journal of Geophysical Research: Oceans |

Volume | 106 |

Issue number | C11 |

State | Published - Nov 15 2001 |

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### ASJC Scopus subject areas

- Geophysics
- Forestry
- Oceanography
- Aquatic Science
- Ecology
- Water Science and Technology
- Soil Science
- Geochemistry and Petrology
- Earth-Surface Processes
- Atmospheric Science
- Earth and Planetary Sciences (miscellaneous)
- Space and Planetary Science
- Palaeontology

### Cite this

*Journal of Geophysical Research: Oceans*,

*106*(C11), 26863-26877. [2000JC000666].