Applied Mathematics and Mechanics

, Volume 13, Issue 1, pp 39–49

Rossby waves with the change of β

  • Liu Shi-kuo
  • Tan Ben-kui

DOI: 10.1007/BF02450427

Cite this article as:
Shi-kuo, L. & Ben-kui, T. Appl Math Mech (1992) 13: 39. doi:10.1007/BF02450427


In this paper, the change of the Rossby parameter β with latitude is considered and the parameter γ≡−dβ/dy=2Ωsinϕ/a2 is introduced and the β-plane approximation is extended into f=f00y-Y0y2/2 which includes the parameter γ. Such approximation closes further to practice especially in the high latitude regions.

We give emphasis to the research of the effect of the parameter γ on the Rossby waves. It is seen that the effect of the parameter γ is remarkable in the high latitude regions. It can produce the Rossby waves caused by the pure parameter γ. And the phase speed formula of Rossby waves with the change of β is generally given, which is degenerated into the well-known Rossby formula when Y0=0. The researches also point out that when the change of β is regarded, even if the basic current ū is a linear function of y the unstable modes can also take place. However, the parameter γ usually plays a stable part in the Rossby waves and it does affect the longitudinal scale and the structure of constant phase lines (trough-ridge lines) of Rossby waves and slow down the growing or decaying of Rossby waves.

Key words

Rossby wavesRossby parameterparameter γ

Copyright information

© Shanghai University of Technology (SUT) 1992

Authors and Affiliations

  • Liu Shi-kuo
    • 1
  • Tan Ben-kui
    • 2
  1. 1.Dept. of GeophysicsPeking UniversityBeijing
  2. 2.Dept. of Atmospheric SciencesNanjing UniversityNanjing