Geostrophic approximation in horizontally differential atmospheric rotation

Masaru Yamamoto, Hiroshi Tanaka

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)273-279
Number of pages7
JournalTheoretical and Applied Mechanics Japan
Publication statusPublished - 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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