Singularity formation in a cylindrical and a spherical vortex sheet
Singularity formation in a cylindrical and a spherical vortex sheet
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圆柱形和球形涡流片中奇点的形成
DOI：
10.1006/jcph.2001.6872
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发表时间：
2001
影响因子：
4.1
通讯作者：
M. Nitsche
中科院分区：
文献类型：
--
作者：
M. Nitsche
本文用数值方法比较了圆柱和球体作冲击运动时产生的平面涡面和轴对称涡面的演化。数值方法解决的困难，发生在轴对称的情况下，对称轴附近。已知平面涡面在有限时间内发展出分支点奇点。平面解和轴对称解的比较表明，轴对称薄片也产生了一个分支点奇异性，并且它与平面奇异性具有相同的p阶。p的值与3/2一致。
Abstract The evolutions of the planar and axisymmetric vortex sheets generated by the impulsive motion of a cylinder and a sphere, respectively, are compared numerically. The numerical method addresses difficulties that occur in the axisymmetric case near the axis of symmetry. The planar vortex sheet is known to develop a branch point singularity in finite time. Comparison of the planar and axisymmetric solutions indicates that the axisymmetric sheet develops a branch point singularity as well, and that it is of the same order p as the planar singularity. The value of p is consistent with 3/2.