### 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) |
---|---|

Pages (from-to) | 139-159 |

Number of pages | 21 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 90 |

Issue number | 3-4 |

State | Published - 1999 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Space and Planetary Science
- Computational Mechanics
- Mechanics of Materials
- Astronomy and Astrophysics

### Cite this

*Geophysical and Astrophysical Fluid Dynamics*,

*90*(3-4), 139-159.

**A reduced model for nonlinear dispersive waves in a rotating environment.** / Milewski, Paul A.; Tabak, Esteban G.

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 90, no. 3-4, pp. 139-159.

}

TY - JOUR

T1 - A reduced model for nonlinear dispersive waves in a rotating environment

AU - Milewski, Paul A.

AU - Tabak, Esteban G.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - Coastal waves

KW - Equatorial waves

KW - Geophysical flows

KW - Nonlinear waves

UR - http://www.scopus.com/inward/record.url?scp=0033406337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033406337&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033406337

VL - 90

SP - 139

EP - 159

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 3-4

ER -