The need to numerically represent a free vortex system arises frequently in fundamental and applied research. Many possible techniques for realizing this vortex system exist but most tend to prioritize accuracy either inside or outside of the vortex core, which therefore makes them unsuitable for a stability analysis considering the entire flow field. In this article, a simple method is presented that is shown to yield an accurate representation of the flow inside and outside of the vortex core. The method is readily implemented in any incompressible Navier–Stokes solver using primitive variables and Cartesian coordinates. It can potentially be used to model a wide range of vortices but is here applied to the case of two helices, which is of renewed interest due to its relevance for wind turbines and helicopters. Three-dimensional stability analysis is performed in both a rotating and a translating frame of reference, which yield eigenvalue spectra that feature both mutual inductance and elliptic instabilities. Comparison of these spectra with available theoretical predictions is used to validate the proposed baseflow model, and new insights into the elliptic instability of curved Batchelor vortices are presented. Furthermore, it is shown that the instabilities in the rotating and the translating reference frames have the same structure and growth rate, but different frequency. A relation between these frequencies is provided.

中文翻译：

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螺旋涡的数值实现：在涡不稳定性中的应用

在基础研究和应用研究中经常需要用数字表示自由涡流系统。存在许多实现这种涡流系统的可能技术，但大多数倾向于优先考虑涡核内部或外部的精度，因此它们不适合考虑整个流场的稳定性分析。在本文中，提出了一种简单的方法，该方法可以准确表示涡核内部和外部的流动。该方法可以使用原始变量和笛卡尔坐标在任何不可压缩的 Navier-Stokes 求解器中轻松实现。它可以潜在地用于模拟范围广泛的涡流，但这里应用于两个螺旋的情况，由于其与风力涡轮机和直升机的相关性，它重新引起了人们的兴趣。三维稳定性分析在旋转和平移参考系中进行，产生具有互感和椭圆不稳定性的特征值谱。这些光谱与可用理论预测的比较用于验证所提出的基流模型，并提出了对弯曲 Batchelor 涡旋椭圆不稳定性的新见解。此外，还表明旋转和平移参考系中的不稳定性具有相同的结构和增长率，但频率不同。提供了这些频率之间的关系。这些光谱与可用理论预测的比较用于验证所提出的基流模型，并提出了对弯曲 Batchelor 涡旋椭圆不稳定性的新见解。此外，还表明旋转和平移参考系中的不稳定性具有相同的结构和增长率，但频率不同。提供了这些频率之间的关系。这些光谱与可用理论预测的比较用于验证所提出的基流模型，并提出了对弯曲 Batchelor 涡旋椭圆不稳定性的新见解。此外，还表明旋转和平移参考系中的不稳定性具有相同的结构和增长率，但频率不同。提供了这些频率之间的关系。