The rolling up of a semi-infinite vortex sheet
The rolling up of a semi-infinite vortex sheet
复制标题
半无限涡片的卷起
DOI：
--
复制
发表时间：
1975
期刊：
影响因子：
--
通讯作者：
D. W. Moore
中科院分区：
文献类型：
--
作者：
D. W. Moore
用解析方法研究了半无限初始直涡面的卷起。在初始状态下，薄层中的环流随距其边缘距离的平方根而增加。以前的研究已经断言，Kaden给出的卷起部分的方程的渐近形式可以通过在局部确定的渐近展开中找到更高的项来改进。这一论断是有争议的，它建议，卡登修正不能被发现，除非整个涡面的形状是已知的。建议的修正使螺旋线的转弯略呈椭圆形，精确的量值涉及整个涡面的积分。虽然一个有用的解析解不能找到这样的方式，它建议的结果将是有用的数值研究。
The rolling up of a semi-infinite initially straight vortex sheet is studied analytically. In its initial state the circulation in the sheet increases as the square root of the distance from its edge. Previous investigations have asserted that the asymptotic form for the equation of the rolled up portion given by Kaden could be improved on by finding higher terms in a locally determined asymptotic expansion. This assertion is contested and it is suggested that the correction to Kaden can not be found unless the shape of the whole vortex sheet is known. The correction proposed renders the turns of the spiral slightly elliptical, the precise magnitude involving an integral over the entire vortex sheet. While a useful analytical solution cannot be found this way, it is suggested that the result would be useful in a numerical study.