论文标题
围绕轴向对称抛物面的弱磁化流的精确分析解决方案，并应用于磁层模型
An exact analytical solution for the weakly magnetized flow around an axially symmetric paraboloid, with application to magnetosphere models
论文作者
论文摘要
具有抛物线形状纵向横截面的旋转对称体经常用于对天体物理物体进行建模，例如磁层和其他钝器物体，并浸入星际或星际气体或血浆流中。我们讨论了一个简单的公式，用于围绕椭圆形抛物面的不可压缩流体的电势流，该抛物线的对称轴与传入流的方向相吻合。规定了这种流动，我们为理想的磁流失动力学的诱导方程提供了一个精确的分析解决方案，以在此流中被动地被动地推动任意方向的最初均匀磁场。我们的解决方案程序基于流的流函数和等距来采用Euler电位和Cauchy的整体形式主义。此外，我们使用一种特定的重新归一化过程，使我们能够生成更通用的分析表达式，以建模由任意标量或矢量值值嵌入在流中的变形，因为它们首先朝向抛物线障碍物，然后超过抛物线障碍物。最后，嵌入其中的速度场和磁场都是从不可压缩到轻度压缩流的概括，其中从伯诺利的原理中发现了相关的密度分布。
Rotationally symmetric bodies with longitudinal cross sections of parabolic shape are frequently used to model astrophysical objects, such as magnetospheres and other blunt objects, immersed in interplanetary or interstellar gas or plasma flows. We discuss a simple formula for the potential flow of an incompressible fluid around an elliptic paraboloid whose axis of symmetry coincides with the direction of incoming flow. Prescribing this flow, we derive an exact analytical solution to the induction equation of ideal magnetohydrodynamics for the case of an initially homogeneous magnetic field of arbitrary orientation being passively advected in this flow. Our solution procedure employs Euler potentials and Cauchy's integral formalism based on the flow's stream function and isochrones. Furthermore, we use a particular renormalization procedure that allows us to generate more general analytical expressions modeling the deformations experienced by arbitrary scalar or vector-valued fields embedded in the flow as they are advected first toward and then past the parabolic obstacle. Finally, both the velocity field and the magnetic field embedded therein are generalized from incompressible to mildly compressible flow, where the associated density distribution is found from Bernoulli's principle.
