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ISSN 1006-9895

CN 11-1768/O4

再论地转流的正压不稳定
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中国科学院大气物理研究所

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Barotropic Instability of Geostrophic Flow: The Problem Revisited
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    摘要:

    文章研究了考虑地转约束的情况下,正压不稳定的必要条件。并基于能量学和位涡动力学理论,对正压不稳定的必要条件的物理含义进行了诠释。对于满足地转平衡的基本流,Rayleigh—Kuo定理修正为:若地转流动可能出现不稳定,基本流的位涡梯度需在某个纬度取极值。Fjortoft定理相应地成为:若地转可能出现不稳定,需满足Qy与U-Us同号。即由原结论中的绝对涡度修正为位涡。这是地转约束也是位涡约束的结果。指出满足能量关系是正压不稳定可能出现的能量学要求,Rayleigh—Kuo定理是正压不稳定可能出现的位涡动力学条件,而Fjortoft定理则是能量学与位涡动力学两种要求的协调,三者均须满足,正压不稳定才有可能发生。

    Abstract:

    Rayleigh-Kuo theorem and Fjortoft theorem provide necessary conditions for barotropic instabilty of a geophysical fluid flow. Moreover, the barotropic instability of the geostrophic flow is of special importance for the geophysical flow. In this paper, two modified necessary conditions for the barotropic instability of the geostrophic flow are obtained. Based on energetics and potential vorticity dynamics theories, the implication of the necessary conditions for barotropic instability is explained. For the geostrophic flow, the Rayleigh-Kuo theorem can be revised as follws: A necessary condition for barotropic instability of the geostrophic flow is that the potential vorticity of the flow should have an extreme point. The Fjortoft theorem correspondingly becomes: A necessary condition for barotropic instability of the geostrophic flow is that Qy(U-Us)>0 in the field of the geostrophic flow, where ys is a point at which Qy=0 and Us=U(ys). That is, the absolute vorticity in the original theorems is modified to potential vorticity. These results are the consequence of geostrophic constraint and potential vorticity constraint. The energy relationship is the energetics requirement for the possibility of barotropic instability, the Rayleigh-Kuo theorem is the potential vorticity dynamics condition for the possibility of barotropic instability, and the Fjortoft theorem is the coordination of the two requirements of energetics and potential vorticity dynamics. For possible barotropic instability, all three requirements must be met.

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  • 收稿日期:2022-01-05
  • 最后修改日期:2022-03-19
  • 录用日期:2022-04-28
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