### Abstract

Effects of horizontally differential atmospheric rotation are considered in geostrophic dynamics of planetary and stellar atmospheres. The Coriolis parameter defined by the angular velocity of a basic flow f and the latitudinal gradient of the angular velocity Γ are used in the present study. Nondimensional differential rotation factor Γ/f and Rossby number R _{o} determine whether the geostrophic approximation can be applied to differential rotations of planetary and stellar atmospheres, or not. When an eddy with small intrinsic phase velocity satisfies the condition of F _{r} ≤ 1 (F _{r}: Froude number) and L/a ≤ R _{o} ≪ 1 (L: eddy horizontal scale, a: planetary radius), for rigid-body rotation (Γ/f ≪ R _{o} ^{2} or Γ/f ∼ R _{o} ^{2}) and weakly differential rotation (Γ/f ∼ R _{o} ^{1}), the geostrophic approximation can be applied. However, for strongly differential rotation (Γ/f ∼ R _{o} ^{0}), the geostrophic approximation cannot be applied, even when R _{o} is sufficiently small.

Original language | English |
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Pages (from-to) | 273-279 |

Number of pages | 7 |

Journal | Theoretical and Applied Mechanics Japan |

Volume | 53 |

Publication status | Published - Dec 1 2004 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Condensed Matter Physics
- Mechanics of Materials

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## Cite this

*Theoretical and Applied Mechanics Japan*,

*53*, 273-279.