Rossby waves with the change of β
- Cite this article as:
- Shi-kuo, L. & Ben-kui, T. Appl Math Mech (1992) 13: 39. doi:10.1007/BF02450427
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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=f0+β0y-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.