Perturbation theory for Rankine vortices
Perturbation theory for Rankine vortices
复制标题
朗肯涡旋的微扰理论
DOI：
10.1017/s0022112099007211
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发表时间：
2000
影响因子：
3.7
通讯作者：
I. Soustova
中科院分区：
文献类型：
--
作者：
K. Gorshkov;L. Ostrovsky;I. Soustova
构造了一个扰动格式来描述在密度分层等扰动作用下稳定的、局部化的朗肯型流体动力学涡的演化。它是基于消除奇异性的扰动，使用必要的正交条件，确定涡流运动。沿着的离散谱模式的线性化问题，可以保持有限的正交条件，连续谱扰动起着至关重要的作用。结果表明，在分层流体中，一个单一的（双）涡可以被破坏，由于后者的模式之前，它的漂移很远，而涡对保持其稳定性较长的时间。后者的运动研究在两种情况下：平滑分层和密度跳跃。对于与界面成小角度的电子对的运动，在我们的理论框架内给出了完整的描述，包括电子对从密度稍大的区域反射的影响。
A perturbation scheme is constructed to describe the evolution of stable, localized Rankine-type hydrodynamic vortices under the action of disturbances such as density stratification. It is based on the elimination of singularities in perturbations by using the necessary orthogonality conditions which determine the vortex motion. Along with the discrete-spectrum modes of the linearized problem which can be kept finite by imposing the orthogonality conditions, the continuous-spectrum perturbations play a crucial role. It is shown that in a stratified fluid, a single (monopole) vortex can be destroyed due to the latter modes before it drifts very far, whereas a vortex pair preserves its stability for a longer time. The motion of the latter is studied in two cases: smooth stratification and a density jump. For the motion of a pair under a small angle to the interface, a complete description is given in the framework of our theory, including the effect of reflection of the pair from a region with slightly larger density.