论文标题
二维电势流使用双色稳定性的稳定性
Stability of Two-dimensional Potential Flows Using Bicomplex Numbers
论文作者
论文摘要
在研究二维不可压缩电势流的研究中，复杂速度电位和复杂速度的使用被广泛传播。使用复杂的分析功能的优点使这种代表了理论空气动力学领域的流动无处不在。但是，这种表示通常不用于线性稳定性研究中，其中大多数作者将速度的表示为实际向量，以允许将扰动表示为复杂的指数函数。在稳定研究中使用复杂速度潜力的一些经典尝试遭受形式错误。在这项工作中，我们提出了一个框架，该框架使用双色编号来对付这两个复杂的表示。该框架适用于vonKármán涡流街的稳定性，并找到了广义公式。结果表明，对称和交错的vonKármán涡流街道的经典结果只是双色配方中广义动力系统的特殊情况。
The use of the complex velocity potential and the complex velocity is widely disseminated in the study of two-dimensional incompressible potential flows. The advantages of working with complex analytical functions made this representation of the flow ubiquitous in the field of theoretical aerodynamics. However, this representation is not usually employed in linear stability studies, where the representation of the velocity as real vectors is preferred by most authors, in order to allow the representation of the perturbation as the complex exponential function. Some of the classical attempts to use the complex velocity potential in stability studies suffer from formal errors. In this work, we present a framework that reconciles these two complex representations using bicomplex numbers. This framework is applied to the stability of the von Kármán vortex street and a generalized formula is found. It is shown that the classical results of the symmetric and staggered von Kármán vortex streets are just particular cases of the generalized dynamical system in bicomplex formulation.
