The elliptical model of two-dimensional vortex dynamics. II: Disturbance equations
The elliptical model of two-dimensional vortex dynamics. II: Disturbance equations
复制标题
二维涡动力学的椭圆模型。
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
B. Legras
中科院分区：
文献类型：
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作者：
D. Dritschel;B. Legras
在第一部分[物理][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体][流体]这些方程采用一组耦合的非线性常微分方程的形式，描述了代表每个漩涡的嵌套椭圆轮廓的质心、纵横比和方向的时间演变。在这里，在第二部分中，将模型扩展到包括对每个轮廓的椭圆形状的扰动，这些扰动是由与其他涡旋的相互作用自然激发的。这种交互作用第一次被明确地计算出来。最后得到的方程解耦成每个模态对称性的方程组，允许对扰动演化进行非常简单的描述。数值试验表明，椭圆模型与完整运动方程在以下四个问题上具有显著的一致性：(1)多线涡族的平衡轮廓形状；(2)多线涡族的线性稳定性。
In Part I [Phys. Fluids A 3, ▪▪▪ (1991)] approximate equations were developed describing the basic evolution of vortices in a general strain field. These equations take the form of a set of coupled, nonlinear ordinary differential equations describing the time evolution of the centroids, aspect ratios, and orientations of a nested set of elliptical contours representing each vortex. Here, in Part II, the model is extended to include disturbances to the elliptical shape of each contour, disturbances that are excited naturally by the interaction with other vortices. This interaction is worked out explicitly for the first time. The final equations obtained decouple into sets of equations for each mode symmetry, allowing for a very simple description of the disturbance evolution. Numerical tests show remarkable agreement between the elliptical model and the full equations of motion in four problems: (1) the equilibrium contour shapes of a multicontour family of vortices, (2) the linear stability of this famil...