### Abstract

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.

Original language | English (US) |
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Pages (from-to) | 139-159 |

Number of pages | 21 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 90 |

Issue number | 3-4 |

DOIs | |

State | Published - 1999 |

### Keywords

- Coastal waves
- Equatorial waves
- Geophysical flows
- Nonlinear waves

### ASJC Scopus subject areas

- Computational Mechanics
- Astronomy and Astrophysics
- Geophysics
- Mechanics of Materials
- Geochemistry and Petrology

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## Cite this

*Geophysical and Astrophysical Fluid Dynamics*,

*90*(3-4), 139-159. https://doi.org/10.1080/03091929908204117