Applied Mathematics and Mechanics

, Volume 13, Issue 1, pp 39–49

Rossby waves with the change of β

  • Liu Shi-kuo
  • Tan Ben-kui


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 waves Rossby parameter parameter γ 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Rossby, C.G., Relations between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action.J. Marine. Res.,2 (1939), 38–55.Google Scholar
  2. [2]
    Charney, J.G., The dynamics of long waves in a baroclinic westerly current,J. Met.,4 (1947), 135–163.MathSciNetGoogle Scholar
  3. [3]
    Phillips, N.A., Elemently Rossby wave,Tellus,17, (1965), 295–301.CrossRefGoogle Scholar
  4. [4]
    Kuo, H.L., Dynamics instability of two-dimensional non-divergent flow in a barotropic atmosphere,J. Met.,6 (1949), 105–122.Google Scholar
  5. [5]
    Zeng, Q.C., The evolution of a Rossby packet wave in a three-dimensional baroclinic atmosphere,J. Atmos. Sci.,40, (1983), 73–84.CrossRefGoogle Scholar

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

Personalised recommendations