The influence of circulation on the stability of vortices to mode-one disturbances
The influence of circulation on the stability of vortices to mode-one disturbances
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DOI：
10.1098/rspa.1995.0153
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发表时间：
1995-12
期刊：
影响因子：
--
通讯作者：
S. G. L. Smith
中科院分区：
文献类型：
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作者：
S. G. L. Smith
二维无粘涡度方程的初值问题是在单调角速度的方位向基本速度场线性化的情况下，对于一阶扰动得到精确解的。利用渐近方法研究了该方程的解的大时间性态。发现基本态的环流决定了扰动的最终命运：对于非零环流的基本态涡度分布，微扰趋于Michalke&Timme(1967)最先提到的定常解，而对于零环流，微扰无限增长。后一种情况对地球物理中孤立涡旋的稳定性具有潜在的重要影响。
The initial value problem for the two-dimensional inviscid vorticity equation, linearized about an azimuthal basic velocity field with monotonic angular velocity, is solved exactly for mode-one disturbances. The solution behaviour is investigated for large time using asymptotic methods. The circulation of the basic state is found to govern the ultimate fate of the disturbance: for basic state vorticity distributions with non-zero circulation, the perturbation tends to the steady solution first mentioned in Michalke & Timme (1967), while for zero circulation, the perturbation grows without bound. The latter case has potentially important implications for the stability of isolated eddies in geophysics.