The stability of planetary waves on an infinite beta‐plane
The stability of planetary waves on an infinite beta‐plane
复制标题
无限β平面上行星波的稳定性
DOI：
10.1080/03091927409365786
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发表时间：
1974
影响因子：
1.3
通讯作者：
A. E. Gill
中科院分区：
文献类型：
--
作者：
A. E. Gill
研究了无限s平面上行星波的稳定性。有两个参数的问题，（a）？= Uκ2/β其中U是行星波的速度振幅，κ是其波数，以及（B）行星波的波数方向。对于较大的M，问题归结为正弦速度分布的瑞利问题。最不稳定波的增长率为0.27 Uκ。由该波损失的能量的38%转移到波数0.59 κ，61%转移到波数1.16 κ。作为？当M值较小时，扰动由两个波组成，它们与主波形成共振相互作用的三波组。讨论了一些地球物理应用。它示出，例如，对于像墨西哥湾流的强电流，这种类型的不稳定性比惯性不稳定性更重要。同时，观察表明主导的漩涡...
The stability of a planetary wave on an infinite s‐plane is examined. There are two parameters in the problem, (a) ? = Uκ2/β where U is the velocity amplitude of the planetary wave and κ its wavenumber, and (b) the direction of the wavenumber of the planetary wave. For large M, the problem reduces to the Rayleigh problem for a sinusoidal velocity distribution. The growth rate of the most unstable wave is 0.27 Uκ. 38 % of the energy lost by this wave is transferred to wavenumber 0.59 κ and 61 % is transferred to wavenumber 1.16 κ. As ? decreases and β effects become more important, there are fewer unstable waves, but unstable waves can always be found. For small M, the disturbance comprises two waves which form a resonantly interacting triad with the primary wave. Some geophysical applications are discussed. It is shown, for instance, that for strong currents like the Gulf Stream, this type of instability is much more important than inertial instability. Also, observations indicate that the dominant eddies...