On the Stability of the Baroclinic Circular Vortex: a Sufficient Criterion for Instability.
On the Stability of the Baroclinic Circular Vortex: a Sufficient Criterion for Instability.
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关于斜压圆形涡旋的稳定性：不稳定的充分判据。
DOI：
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发表时间：
1966
期刊：
影响因子：
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通讯作者：
K. Ooyama
中科院分区：
文献类型：
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作者：
K. Ooyama
本文讨论了轴对称扰动下不可压无粘流体中斜压圆涡的稳定性，证明了在无摩擦时，不稳定性的必要条件也是充分条件。通常的稳定性问题的方法，通过一个单独的，时间依赖的因素的特征值的解决方案是不普遍适用的，因为本征解不一定存在于这个问题。相反，扰动方程的纬向运动被认为是一个初始值问题，并确定一个给定的圆形涡的稳定性从考虑的总动能纬向运动。也就是说，如果对于任何初始扰动扰动，扰动的总动能总是有界的，则涡流被认为是稳定的;如果存在至少一组初始数据，其中扰动的总动能将随时间增加超过极限，则涡流被认为是不稳定的。我...
Abstract The stability of baroclinic circular vortices in an incompressible and inviscid fluid for axially symmetric disturbances is discussed, and the well-known necessary condition for instability is shown to be also a sufficient one in the absence of friction. The customary approach to stability problems by means of the eigen-solution with a separate, time-dependent factor is not generally applicable because eigen-solutions do not necessarily exist in this problem. Instead, the perturbation equation for meridional motion is considered as an initial value problem, and the stability of a given circular vortex is determined from consideration of the total kinetic energy of meridional motion. That is, the vortex is considered stable if the total kinetic energy of the perturbation is always bounded for any initial disturbance; and the vortex is considered unstable if there exists at least one set of initial data for which the total kinetic energy of the perturbation would increase with time beyond limit. Wi...