Formation of curvature singularity along vortex line in an axisymmetric, swirling vortex sheet
Formation of curvature singularity along vortex line in an axisymmetric, swirling vortex sheet
复制标题
轴对称旋转涡流片中沿涡流线曲率奇点的形成
DOI：
10.1063/1.1491255
复制
发表时间：
2002
影响因子：
4.6
通讯作者：
T. Sakajo
中科院分区：
文献类型：
--
作者：
T. Sakajo
我们考虑无粘不可压缩流动中的轴对称、旋转的涡片。Caflisch等人。指出涡片在有限时间内出现奇异性，但并未揭示奇异性的性质。在本文中，我们用与研究二维涡片相同的数值方法，给出了奇点形成的令人信服的数值证据。我们发现，轴对称涡片的径向和轴向分量表现出类似于在许多涡片运动中观察到的二维奇异性，而涡片的方位分量表现出不同的行为。此外，奇异性出现在涡线上，涡片强度的一阶导数形成一个尖点，而已知的奇点与垂直于涡线的曲线上的曲率有关，涡片强度有一个尖点。
We consider an axisymmetric, swirling vortex sheet in an inviscid and incompressible flow. Caflisch et al. pointed out that the vortex sheet acquired a singularity in finite time, but the property of the singularity was not revealed. In the present paper we show convincing numerical evidences of the singularity formation by applying the same numerical methods as what was used in the study of a two-dimensional (2D) vortex sheet. We find that the radial and axial components of the axisymmetric vortex sheet behave like the 2D singularity that has been observed in many vortex-sheet motions, while the azimuthal component of the sheet behaves differently. Furthermore, the singularity appears along the vortex line and the first derivative of the vortex sheet strength forms a cusp, while the known singularities are associated with the curvature along curves perpendicular to the vortex lines and the sheet strength has a cusp.
T. Ishihara：“涡流片三维运动中的奇点形成”J. Fluid Mech.300。
DOI：
--
发表时间：
--
期刊：
影响因子：
--
作者：
通讯作者：
--