### Abstract

The classical Phillips problem of baroclinic instability is generalized, allowing for free deformations of the bottom boundary. The simplicity of the model is exploited to analyze the effects of the variation of the Coriolis parameter with latitude (the so-called β effect) on the stability/instability problem. Conservation laws of energy, momentum, and vorticity-related Casimirs are used to establish nonlinear stability conditions. A spectral analysis reveals that unlike the case of Phillips problem, the β effect can either strengthen or weaken the stability of the basic current, depending on the perturbation scale and the slope of the bottom relative to that of the interface. In particular, the maximal instability occurs in the limit of weak stratification when the planetary and the topographic β effects compensate each other. The maximal unstable wave has an intermediate scale between the internal and the external deformation radii. Nonlinear saturation bounds on unstable basics states are also determined using Shepherd's method. It is found that the enstrophy of the most unstable wave can only be bounded by the total enstrophy of the system.

Original language | English (US) |
---|---|

Article number | 1999JC900192 |

Pages (from-to) | 23357-23366 |

Number of pages | 10 |

Journal | Journal of Geophysical Research C: Oceans |

Volume | 104 |

Issue number | C10 |

State | Published - Oct 15 1999 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Earth and Planetary Sciences (miscellaneous)
- Space and Planetary Science
- Atmospheric Science
- Astronomy and Astrophysics
- Oceanography

### Cite this

*Journal of Geophysical Research C: Oceans*,

*104*(C10), 23357-23366. [1999JC900192].

**Baroclinic instability in a two-layer model with a free boundary and β effect.** / Olascoaga, Maria J; Ripa, P.

Research output: Contribution to journal › Article

*Journal of Geophysical Research C: Oceans*, vol. 104, no. C10, 1999JC900192, pp. 23357-23366.

}

TY - JOUR

T1 - Baroclinic instability in a two-layer model with a free boundary and β effect

AU - Olascoaga, Maria J

AU - Ripa, P.

PY - 1999/10/15

Y1 - 1999/10/15

N2 - The classical Phillips problem of baroclinic instability is generalized, allowing for free deformations of the bottom boundary. The simplicity of the model is exploited to analyze the effects of the variation of the Coriolis parameter with latitude (the so-called β effect) on the stability/instability problem. Conservation laws of energy, momentum, and vorticity-related Casimirs are used to establish nonlinear stability conditions. A spectral analysis reveals that unlike the case of Phillips problem, the β effect can either strengthen or weaken the stability of the basic current, depending on the perturbation scale and the slope of the bottom relative to that of the interface. In particular, the maximal instability occurs in the limit of weak stratification when the planetary and the topographic β effects compensate each other. The maximal unstable wave has an intermediate scale between the internal and the external deformation radii. Nonlinear saturation bounds on unstable basics states are also determined using Shepherd's method. It is found that the enstrophy of the most unstable wave can only be bounded by the total enstrophy of the system.

AB - The classical Phillips problem of baroclinic instability is generalized, allowing for free deformations of the bottom boundary. The simplicity of the model is exploited to analyze the effects of the variation of the Coriolis parameter with latitude (the so-called β effect) on the stability/instability problem. Conservation laws of energy, momentum, and vorticity-related Casimirs are used to establish nonlinear stability conditions. A spectral analysis reveals that unlike the case of Phillips problem, the β effect can either strengthen or weaken the stability of the basic current, depending on the perturbation scale and the slope of the bottom relative to that of the interface. In particular, the maximal instability occurs in the limit of weak stratification when the planetary and the topographic β effects compensate each other. The maximal unstable wave has an intermediate scale between the internal and the external deformation radii. Nonlinear saturation bounds on unstable basics states are also determined using Shepherd's method. It is found that the enstrophy of the most unstable wave can only be bounded by the total enstrophy of the system.

UR - http://www.scopus.com/inward/record.url?scp=0033569005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033569005&partnerID=8YFLogxK

M3 - Article

VL - 104

SP - 23357

EP - 23366

JO - Journal of Geophysical Research: Oceans

JF - Journal of Geophysical Research: Oceans

SN - 2169-9275

IS - C10

M1 - 1999JC900192

ER -