Shape and Stability of Two-Dimensional Uniform Vorticity Regions
Shape and Stability of Two-Dimensional Uniform Vorticity Regions
复制标题
二维均匀涡度区域的形状和稳定性
DOI：
10.7907/nw61-5178
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发表时间：
1987
影响因子：
3.7
通讯作者：
J. Kamm
中科院分区：
文献类型：
--
作者：
J. Kamm
本文研究了不可压缩无粘流体中均匀常涡区域的定常形状、线性稳定性和能量学。Meiron、Saffman和Schatzman [1984]介绍的施瓦茨函数方法用于这些问题的数学表述。数值和分析分析提供了几种配置。对于应变和旋转流场中的单涡，我们找到了从定常椭圆解的分支分叉出来的新解。这些非椭圆稳态被确定为线性不稳定。我们研究了共转涡对，并在数值上证实了Saffman和Szeto [1980]的理论结果，将线性稳定性特征与能量学联系起来。的稳定性性能的无限单个阵列的涡被量化。配对不稳定性被认为是最不稳定的亚谐扰动，并在数值上证实了与面积相关的超谐不稳定性（Saffman和Szeto [1981]）的存在。用椭圆涡模型定性地说明了这些结果。最后，我们研究了不等面积对无限交错双涡列稳定性的影响。我们用数值方法验证了Jimenez [1986 b]的扰动分析结果，表明对于有限但面积不等的涡街，特征次谐波稳定性“交叉”仍然存在。
The steady shapes, linear stability, and energetics of regions of uniform, constant vorticity in an incompressible, inviscid fluid are investigated. The method of Schwarz functions as introduced by Meiron, Saffman and Schatzman [1984] is used in the mathematical formulation of these problems. Numerical and analytical analyses are provided for several configurations. For the single vortex in strained and rotating flow fields, we find new solutions that bifurcate from the branch of steady elliptical solutions. These nonelliptical steady states are determined to be linearly unstable. We examine the corotating vortex pair and numerically confirm the theoretical results of Saffman and Szeto [1980], relating linear stability characteristics to energetics. The stability properties of the infinite single array of vortices are quantified. The pairing instability is found to be the most unstable subharmonic disturbance, and the existence of an area-dependent superharmonic instability (Saffman and Szeto [1981]) is numerically confirmed. These results are exhibited qualitatively by an elliptical vortex model. Lastly, we study the effects of unequal area on the stability of the infinite staggered double array of vortices. We numerically verify the results of the perturbation analysis of Jimenez [1986b] by showing that the characteristic subharmonic stability "cross" persists for vortex streets of finite but unequal areas.