### 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 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Theoretical and Applied Mechanics Japan*,

*53*, 273-279.

**Geostrophic approximation in horizontally differential atmospheric rotation.** / Yamamoto, Masaru; Tanaka, Hiroshi.

Research output: Contribution to journal › Article

*Theoretical and Applied Mechanics Japan*, vol. 53, pp. 273-279.

}

TY - JOUR

T1 - Geostrophic approximation in horizontally differential atmospheric rotation

AU - Yamamoto, Masaru

AU - Tanaka, Hiroshi

PY - 2004/12/1

Y1 - 2004/12/1

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:21244481287

VL - 53

SP - 273

EP - 279

JO - Theoretical and Applied Mechanics

JF - Theoretical and Applied Mechanics

SN - 1348-0693

ER -